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# Integrate the function $x\sin\left(x^2\right)$ from 0 to $\sqrt{\pi }$

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## Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

## Trigonometric Integrals

· Integral of the sine function
$\int\sin\left(\theta \right)dx=-\cos\left(\theta \right)+C$

###  Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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