What is the integral from-pi/3 to pi/3 of 6sec^2(x) ?

The integral from-pi/3 to pi/3 of 6sec^2(x) is 12sqrt(3)

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integral from-pi/3 to pi/3 of 6sec^2(x)

\int_{- \frac{π}{3}}^{\frac{π}{3}} 6 sec^{2} (x) d x

123

Decimal

20.78460 \dots

Solution steps

\int_{- \frac{π}{3}}^{\frac{π}{3}} 6 sec^{2} (x) d x

Take the constant out:

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

= 6 \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)

= 6 [tan (x)]_{- \frac{π}{3}}^{\frac{π}{3}}

Compute the boundaries:

23

= 6 \cdot 23

Simplify

= 123

\int_{0}^{1} 2 y (1 - y) d y

\int_{0}^{5} 2 e^{0.2 t} - t d t

\int_{1}^{2} (3 x^{5} - 2 x^{3}) d x

\int_{0}^{t} e^{a t} d t

\int_{- 1}^{5} 2 x + 6 d x

What is the integral from-pi/3 to pi/3 of 6sec^2(x) ?
The integral from-pi/3 to pi/3 of 6sec^2(x) is 12sqrt(3)