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

The integral from 0 to pi of (2e^x+3sin(x)) is 2e^pi+4

Popular >

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

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

2 e^{π} + 4

Decimal

50.28138 \dots

Solution steps

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

\int_{0}^{π} 2 e^{x} d x = 2 (e^{π} - 1)

\int_{0}^{π} 3 sin (x) d x = 6

= 2 (e^{π} - 1) + 6

Simplify

2 (e^{π} - 1) + 6 : 2 e^{π} + 4

= 2 e^{π} + 4

\int_{0}^{l n (2)} (e^{x} - e^{- x}) d x

\int_{0}^{2} \frac{4}{5 x + 3} d x

\int_{1}^{2} (x + 1) (x^{2} + 2 x)^{2} d x

\int_{- π}^{π} x^{3} sin (x) d x

\int_{0}^{\frac{π}{4}} 9 sec^{2} (t) d t

What is the integral from 0 to pi of (2e^x+3sin(x)) ?
The integral from 0 to pi of (2e^x+3sin(x)) is 2e^pi+4