`int_0^(pi/4)(sec^2 (t))dt` Evaluate the integral.

Textbook Question

Chapter 5, 5.3 - Problem 31 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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lemjay | High School Teacher | (Level 3) Senior Educator

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`int_0^(pi/4) sec^2(t) dt`

Take note that the derivative of tangent is d/(d theta) tan (theta)= sec^2 (theta).

So taking the integral of sec^2(t) result to:

`= tan (t) |_0^(pi/4)`

Plug-in the limits of integral as follows `F(x)=int_a^b f(x) dx= F(b)-F(a)` .

`=tan (pi/4)-tan(0)`

`=1-0`

`=1`

Therefore,  `int_0^(pi/4) sec^2(t) dt = 1` .

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