What is the integral from 0 to 1 of 3x+cos(3x-3) ?

The integral from 0 to 1 of 3x+cos(3x-3) is 3/2+1/3 sin(3)

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integral from 0 to 1 of 3x+cos(3x-3)

\int_{0}^{1} 3 x + cos (3 x - 3) d x

\frac{3}{2} + \frac{1}{3} sin (3)

Decimal

1.54704 \dots

Solution steps

\int_{0}^{1} 3 x + cos (3 x - 3) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} 3 x d x + \int_{0}^{1} cos (3 x - 3) d x

\int_{0}^{1} 3 x d x = \frac{3}{2}

\int_{0}^{1} cos (3 x - 3) d x = \frac{1}{3} sin (3)

= \frac{3}{2} + \frac{1}{3} sin (3)

\int_{0}^{\frac{π}{2}} x^{2} d x

\int_{4}^{6} (x^{2} + 2 x - 7) d x

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

\int_{4}^{6} (x^{2} + 2 x - 6) d x

\int_{0}^{10} x e^{1 - x^{2}} d x

What is the integral from 0 to 1 of 3x+cos(3x-3) ?
The integral from 0 to 1 of 3x+cos(3x-3) is 3/2+1/3 sin(3)