JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \({\int\limits_0^x {\left| {\cos \,x} \right|} ^3}\,dx\) is
- A \(0\)
- B \(\frac{4}{3}\)
- C \(\frac{2}{3}\)
- D \(-\frac{4}{3}\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(\int\limits_0^{\frac{\pi }{2}} {\left( {{{\left| {\cos x} \right|}^3} + {{\left| {\cos \left( {\pi - x} \right)} \right|}^3}} \right)} dx\) \( \Rightarrow 2\int\limits_0^{\frac{\pi }{2}} {{{\left| {\cos x} \right|}^3}} dx\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- For all \(z \in C\) on the curve \(C _1:| z |=4\), let the locus of the point \(z +\frac{1}{ z }\) be the curve \(C _2\). ThenJEE Mains 2023 Hard
- The area of the region \(A\,\{ \,(x,y)\,\,:\,\,0\,\, \le \,y\, \le \,x\,\left| x \right|\, + \,1\) and \( - \,1\, \le \,x\, \le \,1\,\} \) in sq. units, isJEE Mains 2019 Hard
- All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of \(10\) to each of the students. Which of the following statistical measures will not change even after the grace marks were given \(?\)JEE Mains 2013 Easy
- If \(5, 5r, 5r^2\) are the lengths of the sides of a triangle, then \(r\) cannot be equal toJEE Mains 2019 Hard
- Let \(\vec a = \hat i - \hat j,\) \(\vec b = \hat i + \hat j + \hat k\) and \(\vec c\) be a vector such that \(\vec a \times \vec c + \vec b = 0\) and \(\vec a.\vec c = 4\), then \({\left| {\vec c} \right|^2}\) is equal toJEE Mains 2019 Hard
- Let \(C\) be a circle having centre in the first quadrant and touching the \(x\)-axis at a distance of \(3\) units from the origin. If the circle \(C\) has an intercept of length \(6\sqrt{3}\) on \(y\)-axis, then the length of the chord of the circle \(C\) on the line \(x - y = 3\) is :JEE Mains 2026 Medium
More PYQs from JEE Mains
- The area of the region \(\{(x, y) : x^2 - 8x \leq y \leq -x\}\) is :JEE Mains 2026 Medium
- If \(y(\theta)=\frac{2 \cos \theta+\cos 2 \theta}{\cos 3 \theta+4 \cos 2 \theta+5 \cos \theta+2}\) then at \(\theta=\frac{\pi}{2}, y^{\prime \prime}+y^{\prime}+y\) is equal to :JEE Mains 2024 Hard
- Let \(O\) be the origin and \(OP\) and \(OQ\) be the tangents to the circle \(x^2+y^2-6 x+4 y+8=0\) at the point \(P\) and \(Q\) on it. If the circumcircle of the triangle OPQ passes through the point \(\left(\alpha, \frac{1}{2}\right)\), then a value of \(\alpha\) isJEE Mains 2023 Hard
- If \(A=\left(\begin{array}{cc}0 & \sin \alpha \\ \sin \alpha & 0\end{array}\right)\) and \(\operatorname{det}\left(A^{2}-\frac{1}{2} I\right)=0,\) then a possible value of \(\alpha\) isJEE Mains 2021 Medium
- Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group \(A\) and the remaining 3 from group \(B\), is equal to :JEE Mains 2025 Easy
- Let \(O\) be the origin. Let \(\overline{ OP }= x \hat{ i }+ y \hat{ j }-\hat{ k }\) and \(\overline{ OQ }=-\hat{ i }+2 \hat{ j }+3 x \hat{ k }, x , y \in R , x >0,\) be such that \(|\overline{ PQ }|=\sqrt{20}\) and the vector \(\overline{ OP }\) is perpendicular to \(\overline{ OQ }\). If \(\overline{ OR }=3 \hat{ i }+ z \hat{ j }-7 \hat{ k }, z \in R ,\) is coplanar with \(\overline{ OP }\) and \(\overline{ OQ },\) then the value of \(x ^{2}+ y ^{2}+ z ^{2}\) is equal to ...... .JEE Mains 2021 Hard