`int_0^(pi/4)(sec(theta)tan(theta))d theta` Evaluate the integral.

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Chapter 5, 5.3 - Problem 32 - 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 (theta) tan (theta)) d theta`

Take note that the derivative of secant is `d/(d theta) (sec (theta)) = sec(theta) tan (theta)` .

So taking the integral of sec(theta) tan(theta) result to:

`=sec (theta) |_0^(pi/4)`

Then, plug-in the limits of the integral as follows `F(x) = int f(x) dx = F(b)-F(a)` .

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

`=sqrt2-1`

Therefore, `int_0^(pi/4) (sec (theta)tan(theta)) d theta =sqrt2-1` .

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