What is the integral from 1 to 10 of cos(2x) ?

The integral from 1 to 10 of cos(2x) is 1/2 (sin(20)-sin(2))

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integral from 1 to 10 of cos(2x)

\int_{1}^{10} cos (2 x) d x

\frac{1}{2} (sin (20) - sin (2))

Decimal

0.00182 \dots

Solution steps

\int_{1}^{10} cos (2 x) d x

Apply u-substitution

: \int_{2}^{20} cos (u) \frac{1}{2} d u

= \int_{2}^{20} cos (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{2}^{20} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{2}^{20}

Compute the boundaries:

sin (20) - sin (2)

= \frac{1}{2} (sin (20) - sin (2))

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

\int_{1}^{4} \frac{x ^{2}}{x} d x

\int_{0}^{1} e^{1 - t} d t

\int_{2}^{5} 5 x^{2} d x

\int_{- 2}^{1} 4 d x

What is the integral from 1 to 10 of cos(2x) ?
The integral from 1 to 10 of cos(2x) is 1/2 (sin(20)-sin(2))