`int_0^(pi/4) cscx dx` Decide whether the integral is improper. Explain your reasoning

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The integral `int_0^(pi/4)csc x dx` is improper because cosecant is not defined on zero (more generally `csc x` is not defined for `x in {k pi, k in ZZ}.`) and the interval of integration includes that point.

The image below shows graph of the function over `[-pi/4,pi/4].` As we can see 

`lim_(x to 0)csc x=+-infty.`  We can also see, from the image, that the above integral will diverge or more precisely it will be equal to infinity.                                                   

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Images:
Image (1 of 1)
Approved by eNotes Editorial