What is the integral from 0 to 3 of (2sin(x)-e^x) ?

The integral from 0 to 3 of (2sin(x)-e^x) is 3-2cos(3)-e^3

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integral from 0 to 3 of (2sin(x)-e^x)

\int_{0}^{3} (2 sin (x) - e^{x}) d x

3 - 2 cos (3) - e^{3}

Decimal Notation

- 15.10555 \dots

Solution steps

\int_{0}^{3} 2 sin (x) - e^{x} 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}^{3} 2 sin (x) d x - \int_{0}^{3} e^{x} d x

\int_{0}^{3} 2 sin (x) d x = 2 (- cos (3) + 1)

\int_{0}^{3} e^{x} d x = e^{3} - 1

= 2 (- cos (3) + 1) - (e^{3} - 1)

Simplify

2 (- cos (3) + 1) - (e^{3} - 1) : 3 - 2 cos (3) - e^{3}

= 3 - 2 cos (3) - e^{3}

n = 1 \sum \infty \frac{1}{n} \cdot (- 1)^{n}

\int \frac{sin ( 2 x )}{10 + cos ^{2} ( x )} d x

\frac{s + 2}{s ^{2} + 2 s + 5} \cdot \frac{1}{s}

\frac{d ^{2}}{d x ^{2}} (\frac{2}{x})

\int (\frac{sin ( x )}{x})^{2} d x

What is the integral from 0 to 3 of (2sin(x)-e^x) ?
The integral from 0 to 3 of (2sin(x)-e^x) is 3-2cos(3)-e^3