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Definite Integration question

2021 · 26 Feb · Shift 1 · Q37

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Definite Integration
2021 · 26 Feb · Shift 1 · Q37

Definite Integration question

2021 · 26 Feb · Shift 1 · Q37

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

The value of the integral

\int\limits_0^\pi {|{{\sin }\,}2x|dx}

is

\underline{\hspace{2cm}}

.

Numerical answer

View written solutionFree

Correct answer: 2

We need to evaluate $I=\int_0^\pi |\sin 2x|\,dx.$
Let $u=2x \implies du=2dx \implies dx=\frac{du}{2}.$ When $x=0$ , $u=0$ ; when $x=\pi$ , $u=2\pi$ .

So, $I=\int_0^\pi |\sin 2x|\,dx=\frac12\int_0^{2\pi}|\sin u|\,du.$

Now use the standard result: $\int_0^{2\pi} |\sin u|\,du=4,$ because over one full period, the area under $|\sin u|$ is $4$ .

Therefore, $I=\frac12\cdot 4=2.$

Hence the required integer value is $\boxed{2}.$

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