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Step-by-step Solution

Integrate $x\sqrt{1+2x^2}$ from $0$ to $2$

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Answer

$4.3333$

Step-by-step explanation

Problem to solve:

$\int_0^2\left(x\sqrt{1+2x^2}\right)dx$
1

Solve the integral $\int_{0}^{2} x\sqrt{1+2x^2}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=1+2x^2 \\ du=4xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{4x}=dx$

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Answer

$4.3333$
$\int_0^2\left(x\sqrt{1+2x^2}\right)dx$

Main topic:

Definite integrals

Used formulas:

4. See formulas

Time to solve it:

~ 0.78 seconds

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