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

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Answer 1 · 2015-02-20T16:17:59

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 :

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

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

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

How do I evaluate int_0^5(2 e^x + 5cos(x)) dxint_0^5(2 e^x + 5cos(x)) dx?