Consider the following statements: 1. $\mathop \smallint \nolimits_{ - \pi /2}^{\pi /2} \,\,\sqrt {\cos \,\,x\,\, - \,\,{{\cos }^3}\,\,x} \,dx = \frac{3}{4}$ 2. $\mathop \smallint \nolimits_0^4 \,\,\left( {\,\left| {\,x - 1\,} \right|\,\, + \,\,\left| {\,x - 3\,} \right|\,} \right)dx = 10$ Which of these is/are correct?

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Consider the following statements:
1.

\int \nolimits_{ - \pi /2}^{\pi /2} \,\,\sqrt {\cos \,\,x\,\, - \,\,{{\cos }^3}\,\,x} \,dx = \frac{3}{4}

\int \nolimits_0^4 \,\,\left( {\,\left| {\,x - 1\,} \right|\,\, + \,\,\left| {\,x - 3\,} \right|\,} \right)dx = 10

Which of these is/are correct?

View answer and explanation

Correct option: B

Only

\left( \mathrm{2} \right)

Option B (Only (2)) is correct because statement 2 is true after evaluating the integral, while statement 1 is false.