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

The integral from pi/4 to pi/3 of-sec^2(θ) is -sqrt(3)+1

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integral from pi/4 to pi/3 of-sec^2(θ)

\int_{\frac{π}{4}}^{\frac{π}{3}} - sec^{2} (θ) d θ

- 3 + 1

Decimal

- 0.73205 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{3}} - sec^{2} (θ) d θ

Take the constant out:

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

= - \int_{\frac{π}{4}}^{\frac{π}{3}} sec^{2} (θ) d θ

Use the common integral:

\int sec^{2} (θ) d θ = tan (θ)

= - [tan (θ)]_{\frac{π}{4}}^{\frac{π}{3}}

Compute the boundaries:

3 - 1

= - (3 - 1)

Simplify

= - 3 + 1

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\int_{- 4}^{0} 2 x^{3} + 12 x^{2} + 16 x d x

What is the integral from pi/4 to pi/3 of-sec^2(θ) ?
The integral from pi/4 to pi/3 of-sec^2(θ) is -sqrt(3)+1