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• Math
`int_1^2(1+2y)^2dy` `=int_1^2((1)^2+2*2y*1+(2y)^2)dy` `=int_1^2(1+4y+4y^2)dy` `=[y+4y^2/2+4y^3/3]_1^2` `=[y+2y^2+(4y^3)/3]_1^2` `=[2+2(2)^2+(4(2^3))/3]-[1+2(1)^2+(4(1)^3)/3]`...

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• Math
`int_1^4(5-2t+3t^2)dt` apply the sum rule and power rule, `=[5t-2t^2/2+3t^3/3]_1^4` `=[5t-t^2+t^3]_1^4` `=[5*4-4^2+4^3]-[5*1-1^2+1^3]` `=(20-16+64)-(5-1+1)` `=(84-16)-(5)` =63

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• Math
`int_0^1(1+(1/2)u^4+(2/5)u^9)du` `=[u+(1/2)(u^(4+1)/(4+1))+(2/5)(u^(9+1)/(9+1))]_0^1` `=[u+u^5/10-u^10/25]_0^1 = [1+1^5/10-1^10/25]-[0+0^5/10-0^10/25]` `=(1+1/10-1/25)` `=(50+5-2)/50` =53/50

Asked by enotes on via web

• Math
You need to evaluate the definite integral such that: `int_1^9 sqrt x dx = (x^(3/2))/(3/2)|_1^9` `int_1^9 sqrt x dx = (2/3)(9sqrt9 - 1sqrt1)` `int_1^9 sqrt x dx = (2/3)(27-1)` `int_1^9 sqrt x dx...

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• Math
Evaluate `int_1^8(x^(-2/3))dx` Integrate the function. `inta^n=a^(n+1)/(n+1)` `=x^(1/3)/(1/3)=3x^(1/3)` Evaluate the function from x=1 to x=8. `=3[8^(1/3)-1^(1/3)]` `=3[2-1]` =3

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=sqrt(t^2+4)` and `g(x)=F_0(x).`...

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• Math
`F(x)=int_x^pisqrt(1+sec(t))dt` `F(x)=-int_pi^xsqrt(1+sec(t))dt` `F'(x)=-d/dxint_pi^xsqrt(1+sec(t))dt` `F'(x)=-sqrt(1+sec(x))`

Asked by enotes on via web

• Math
You need to use the Part 1 of the FTC to evaluate the derivative of the function. You need to notice that the function G(x) is the composite of two functions `f(x) = int_1^x cos t dt ` and `g(x) =...

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=ln(t)` and `h(x)=F_1(e^x).` Therefore...

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=t^2/(t^4+1)` and `h(x)=F_1(sqrt(x))`...

Asked by enotes on via web

• Math
You need to use the Part 1 of the FTC to evaluate the derivative of the function. You need to notice that the function y is the composite of two functions `f(x) = int_1^x sqrt(1+sqrt t) dt` and...

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=cos^2(t)` and `y(x)=F_0(x^4).` Therefore...

Asked by enotes on via web

• Math
`y=int_(1-3x)^1(u^3/(1+u^2))du` Let t=1-3x `dt/dx=-3` `dy/dx=dy/dt*dt/dx` `y'=d/dxint_(1-3x)^1(u^3/(1+u^2))du` `=d/dtint_t^1(u^3/(1+u^2))du.dt/dx` `=-d/dtint_1^t(u^3/(1+u^2))du.dt/dx`...

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• Math
You need to use the Part 1 of the FTC to evaluate the derivative of the function. You need to notice that the function h(x) = y is the composite of two functions `f(x) = int_1^x sqrt(1+t^2)dt` and...

Asked by enotes on via web

• Math
You need to evaluate the integral, such that: `int_(-1)^2(x^3 - 2x)dx = int_(-1)^2 x^3 dx - int_(-1)^2 2x dx` `int_(-1)^2(x^3 - 2x)dx = (x^4/4 - x^2)|_(-1)^2` `int_(-1)^2(x^3 - 2x)dx = (2^4/4 - 2*2...

Asked by enotes on via web

• Math
`int_(-1)^1 x^100 dx` To evaluate this, apply the formula `int x^n dx = x^(n+1)/(n+1)` . `= x^101/101 |_(-1)^1` Then, plug-in the limits of the integral as follows `F(x) =int_a^bf(x) dx = F(b)-...

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=1/(t^3+1)` and `g(x)=F_1(x).` Therefore...

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=e^(t^2-t)` and `g(x)=F_3(x).` Therefore...

Asked by enotes on via web

• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f` `F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.` Here `f(t)=(t-t^2)^8` and `g(x)=F_5(x).` Therefore...

Asked by enotes on via web

• History
There are many different ways to answer this question. Let us look at a few. One way to answer this is to say that Thanksgiving is celebrated as a way of emulating the Pilgrims who were some of...

Asked by enotestest on via web

• Aristotle
Aristotle was a Greek philosopher. He was mentored by Plato and went on to become the mentor and tutor of Alexander the Great. His philosophical foundations draw upon a variety of sources including...

Asked by user2337386 on via web

• Politics
The problem with defining the term "extremist political organization" is that it is by nature one applied only in the second or third person. In other words, the word "extremism" is one we do not...

Asked by stariq1998 on via web

• Social Sciences
Compatibilism attempts to resolve the problem of free will and determinism by proposing that the two positions are compatible. Specifically, it asserts that: Determinism is true, that is, all human...

Asked by tracey1966 on via web

• History
Lincoln's Thanksgiving Proclamation, which declared the final day of November a national day of "thanksgiving and praise to Almighty God," was one of many similar declarations by American...

Asked by enotestest on via web

• History
Columbus's motivation for his voyage was to reach Asia by sailing west. Neither he nor his backers (nor the people who thought his voyage ill-advised) knew that he would reach the "New World" by...

Asked by enotes on via web

• Macbeth
In Act 2, Scene 2, Macbeth meets Lady Macbeth having just "done the deed" (killed Duncan and his guards). Both Macbeth and Lady Macbeth are very much on edge. Lady Macbeth's confidence is shaken...

Asked by bushpab on via web

• Reference
Space exploration's values divide into two categories: human curiosity, and free enterprise (capitalism). The first category holds scientific inquiry -- how does the universe work? What are the...

Asked by enotes on via web

• Health
To evaluate an article from the perspective of what you and I find confusing or surprising about the content, we usually have to ask ourselves certain questions: 1)Does the author state his/her...

• 1984
One of the ideas prevalent in 1984 is the idea of the government controlling the people. When Winston is talking to Julia about the war, she expresses the opinion that it is not real. “The...

Asked by user5708261 on via web

• Of Mice and Men
Crooks is the only farmhand who is African American. Living as a black man in the Depression Era, and among a bunch of rogue men of their generation, rendered Crooks as an outsider to the group....

• A Midsummer Night's Dream
Theseus first sides with Egeus and tells Hermia to obey him, and then changes his mind and overrules Egeus to tell her she can marry Lysander. Theseus either contradicts himself or changes his mind...

Asked by enotes on via web

• Misery
The ending of "Misery" is not a happy one, but it is realistic. The poor man can't get anybody to listen to his grief. Nobody cares about him. This seems to be the way of the world. If he were a...

Asked by user6519295 on via web

• History
World War II was fought for many reasons, stretching back to the end of World War I. But the main cause of World War II was the rise of dictatorships in the 1930s. There were dictators in many...

Asked by enotes on via web

• Of Mice and Men
Candy’s dog is old and smelly, and for this reason Carlson shoots it. Candy is the old swamper, and he has a very old dog. The dog is considered too old and smelly, and Carlson offers to shoot...

Asked by enotes on via web

• Hamlet
In Act 1, Scene 1, there is nothing that speaks directly to Hamlet's lack of trust in himself. The scene mostly features the ghost (of Old Hamlet) and how Bernardo, Horatio, and Marcellus react to...

Asked by chloecool99 on via web

• Macbeth
Fleance escapes because the witches pronounce that Banquo’s sons will be king. Aside from the purposes of historical accuracy, Fleance needs to escape so that all three of the witches' original...

Asked by enotes on via web

• History
This phrase is found in the opening passage of the Declaration, where Jefferson is explaining why a declaration is needed in the first place. In this context "station" means something like "status"...

Asked by user3293309 on via web

• Thank You, M'am
In Thank You, M'am by Langston Hughes, the reader is immediately introduced to Mrs. Luella Bates Washington Jones and can form an opinion of her quite readily. The fact that her purse contains a...

Asked by mohandhuroon13 on via web

• Science
The term "mRNA" stands for "messenger RNA." This is usually enough of a hint to remember their function; to carry messages in the body, specifically messages for creating proteins. The mRNA is like...

Asked by lovelyzebra16 on via web

• Stopping by Woods on a Snowy Evening
‘Stopping by woods’ may appear to be a simple and small poem, yet one can unravel deeper and serious themes running through it. The beauty of the woods is so fascinating that the traveler...

• The Open Boat
One of the ways the author illustrates the daunting task ahead of the men is to make the ocean like a character. Each wave is a "menace." As each salty wall of water approached, it shut all else...

Asked by ryankirchner10 on via web

• Rebecca Skloot
Yes, there were several success stories in The Immortal Life of Henrietta Lacks. Henrietta's daughter, Deborah, struggled to understand the entire notion of her mother's cells continuing to "live"....

Asked by samindermalhi on via web

• Macbeth
The queen, Duncan’s wife and Malcolm and Donalbain’s mother, is dead. Although there is a king at the beginning of the play, there is no mention of the queen. Malcolm and Donalbain obviously...

Asked by amdid2 on via web

• Reference
Malaysia’s economical woes can be traced back to the Chinese economic slowdown. The country is one of the China’s largest trading partners and the ripples of the downturn in China were bound to...

Asked by fangjx97 on via web

• History
President Kennedy’s inaugural address is important in our daily lives. This address focused on the defense of liberty and freedom. It sent a message throughout the world that the United States...

Asked by shyanneg01 on via web

• History
The word "imperialism" describes a process where a nation attempts to expand its influence beyond its own borders by gaining control of territories or peoples. This can come in a number of...

Asked by s157006 on via web

• Winter Dreams
Dexter's general feeling about winter is that it engulfs and shadows the beauty of summertime. In the story, we read that Dexter usually breaks out his skis when 'the long, Minnesota winter shut(s)...

Asked by th3p00kie on via web

• On My First Son
Before I answer that question, let's review the definition of "tone". Tone is a literary device that indicates the emotion the author intends to communicate in his/her work, conveyed through word...

Asked by awesomesinger33 on via web

• A Doll's House
Main Theme The most salient common theme shared among the female characters found in the short story "The Yellow Wallpaper" by Charlotte Perkins Gilman, the play A Doll's House by Henrik Ibsen, and...

Asked by wooka7685 on via web