Question

How do I evaluate `int_0^5(2 e^x + 5cos(x)) dx`?

Answer 1

Hello !

Answer. 2e^5 + 5sin(5) - 2.

Explanation Take antiderivative of `x\mapsto e^x` and `x\mapsto cos(x)` and use the linearity of integral :

`\int_0^5 (2e^x + 5cos(x)) dx = [2e^x + 5sin(x)]_0^5`

`\int_0^5 (2e^x + 5cos(x)) dx = (2e^5 + 5sin(5)) - (2e^0 + 5sin(0))`

`\int_0^5 (2e^x + 5cos(x)) dx = 2e^5 + 5sin(5) - 2`.