What is the integral from 0 to 2a of e^xx^2 ?

The integral from 0 to 2a of e^xx^2 is 4a^2e^{2a}-2(2ae^{2a}-e^{2a})-2

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integral from 0 to 2a of e^xx^2

\int_{0}^{2 a} e^{x} x^{2} d x

4 a^{2} e^{2 a} - 2 (2 a e^{2 a} - e^{2 a}) - 2

Solution steps

\int_{0}^{2 a} e^{x} x^{2} d x

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{2 a}

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{2 a}

\int 2 x e^{x} d x = 2 (e^{x} x - e^{x})

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{2 a}

Compute the boundaries:

4 a^{2} e^{2 a} - 2 (2 a e^{2 a} - e^{2 a}) - 2

= 4 a^{2} e^{2 a} - 2 (2 a e^{2 a} - e^{2 a}) - 2

\int_{- 2}^{2} - 5 - x^{2} d x

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\int_{- 2}^{2} 4 + y^{2} - 2 y^{2} d y

What is the integral from 0 to 2a of e^xx^2 ?
The integral from 0 to 2a of e^xx^2 is 4a^2e^{2a}-2(2ae^{2a}-e^{2a})-2