What is the integral from 0 to pi/4 of 1/(cos^2(x)) ?

The integral from 0 to pi/4 of 1/(cos^2(x)) is 1

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integral from 0 to pi/4 of 1/(cos^2(x))

\int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( x )} d x

1

Solution steps

\int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( x )} d x

Use the common integral:

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= [tan (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

1

= 1

\int_{1}^{\infty} x^{2} e^{- x} d x

\int_{- 2}^{3} e^{\frac{x}{2}} d x

\int_{1}^{6} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\int_{0}^{1} (x - 1) d x

\int_{0}^{1} x ln (1 + x) d x

What is the integral from 0 to pi/4 of 1/(cos^2(x)) ?
The integral from 0 to pi/4 of 1/(cos^2(x)) is 1