What is the integral from 0 to pi/4 of 5sec^2(x) ?

The integral from 0 to pi/4 of 5sec^2(x) is 5

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integral from 0 to pi/4 of 5sec^2(x)

\int_{0}^{\frac{π}{4}} 5 sec^{2} (x) d x

5

Solution steps

\int_{0}^{\frac{π}{4}} 5 sec^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{\frac{π}{4}} sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= 5 [tan (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

1

= 5 \cdot 1

Simplify

= 5

\int \frac{1}{x ^{2} x ^{2} + 4} d x

y^{^{'}} + 4 x^{3} y^{2} = 0

\frac{\partial}{\partial x} (x^{2} - 5 x^{2} y - 6 x y^{2})

\int \frac{x ^{2} - x}{1 + 3 x ^{2} - 2 x ^{3}} d x

y = (x^{2} + 1)

What is the integral from 0 to pi/4 of 5sec^2(x) ?
The integral from 0 to pi/4 of 5sec^2(x) is 5