What is the integral from 0 to pi/3 of (4sec^2(x)) ?

The integral from 0 to pi/3 of (4sec^2(x)) is 4sqrt(3)

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integral from 0 to pi/3 of (4sec^2(x))

\int_{0}^{\frac{π}{3}} (4 sec^{2} (x)) d x

43

Decimal

6.92820 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 4 sec^{2} (x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{\frac{π}{3}} sec^{2} (x) d x

Use the common integral:

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

= 4 [tan (x)]_{0}^{\frac{π}{3}}

Compute the boundaries:

3

= 43

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What is the integral from 0 to pi/3 of (4sec^2(x)) ?
The integral from 0 to pi/3 of (4sec^2(x)) is 4sqrt(3)