What is the integral from 0 to pi/3 of 5sec^2(x) ?

The integral from 0 to pi/3 of 5sec^2(x) is 5sqrt(3)

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integral from 0 to pi/3 of 5sec^2(x)

\int_{0}^{\frac{π}{3}} 5 sec^{2} (x) d x

53

Decimal Notation

8.66025 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 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}{3}} sec^{2} (x) d x

Use the common integral:

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

= 5 [tan (x)]_{0}^{\frac{π}{3}}

Compute the boundaries:

3

= 53

\int_{- 3}^{3} x^{\frac{1}{3}} d x

\int_{0}^{2} \frac{y ^{2}}{y ^{3} + 1} d y

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

\int_{0}^{2 π} - 4 sin^{2} (t) d t

\int_{0}^{3} x^{2} - 3 x + 2 d x

What is the integral from 0 to pi/3 of 5sec^2(x) ?
The integral from 0 to pi/3 of 5sec^2(x) is 5sqrt(3)