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

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

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

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

43

Decimal

6.92820 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 2 [tan (x)]_{- \frac{π}{3}}^{\frac{π}{3}}

Compute the boundaries:

23

= 2 \cdot 23

Simplify

= 43

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