What is the integral from (3pi)/2 to pi/2 of cos(x) ?

The integral from (3pi)/2 to pi/2 of cos(x) is 2

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integral from (3pi)/2 to pi/2 of cos(x)

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

2

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Use the common integral:

\int cos (x) d x = sin (x)

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

Compute the boundaries:

- 2

= - (- 2)

Simplify

= 2

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

\int_{0}^{2} x + 6 - x^{3} d x

\int_{0}^{\frac{π}{4}} cos (2 x) d x

\int_{0}^{4} π (3 x^{2})^{2} d x

\int_{1}^{10} t d t

What is the integral from (3pi)/2 to pi/2 of cos(x) ?
The integral from (3pi)/2 to pi/2 of cos(x) is 2