What is the integral from 0 to pi/2 of 2cos(t) ?

The integral from 0 to pi/2 of 2cos(t) is 2

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integral from 0 to pi/2 of 2cos(t)

\int_{0}^{\frac{π}{2}} 2 cos (t) d t

2

Solution steps

\int_{0}^{\frac{π}{2}} 2 cos (t) d t

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{π}{2}} cos (t) d t

Use the common integral:

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

= 2 [sin (t)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{\frac{1}{2}}^{x} \frac{2}{t ^{2}} d t

\int_{0}^{1} \frac{x}{2 x + 1} d x

\int_{0}^{3} x e^{- 0.4 x} d x

\int_{0}^{3} \frac{x}{16 - x ^{2}} d x

\int_{1}^{8} \frac{ln ( x )}{x} d x

What is the integral from 0 to pi/2 of 2cos(t) ?
The integral from 0 to pi/2 of 2cos(t) is 2