To determine

To evaluate:

The integral ∫-10102exsinh⁡x+cosh⁡x dx

Answer

40

Explanation

1) Concept:

i) Indefinite Integral

∫ex dx=ex+C

2) Given:

∫-10102exsinh⁡x+cosh⁡x dx

3) Calculation:

We know that,sinh⁡x=ex-e-x2 and cosh⁡x=ex+e-x2

Substitute sinh⁡x and cosh⁡x in given integral.

∫-10102exsinh⁡x+cosh⁡x dx=∫-10102exex-e-x2+ex+e-x2 dx

=∫-10102exex-e-x+ex+e-x2 dx

By simplification,

=∫-10102exex dx

=∫-10102 dx

By using concept i), and fundamental theorem of calculus

=2x-1010

=2x-1010

=2(10--10)

=40

Conclusion:

∫2exsinh⁡x+cosh⁡x dx=40