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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
The value of ${\int\limits_0^x {\left| {\cos \,x} \right|} ^3}\,dx$ is
  • ✓
    $0$
  • B
    $\frac{4}{3}$
  • C
    $\frac{2}{3}$
  • D
    $-\frac{4}{3}$
✓

Answer

Correct option: A.
$0$
a
$\int\limits_0^{\frac{\pi }{2}} {\left( {{{\left| {\cos x} \right|}^3} + {{\left| {\cos \left( {\pi  - x} \right)} \right|}^3}} \right)} dx$

$ \Rightarrow 2\int\limits_0^{\frac{\pi }{2}} {{{\left| {\cos x} \right|}^3}} dx$

$ \Rightarrow 2\int\limits_0^{\frac{\pi }{2}} {{{\left( {\cos x} \right)}^3}} dx$

$\Rightarrow 2\left(\frac{2}{3}\right)=\frac{4}{3} \text { (By wallis formula) }$

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