MHT CET · Maths · Definite Integration
\(\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \sin ^{-4} x \mathrm{~d} x=\)
- A \(\frac{8}{3}\)
- B \(-\frac{8}{3}\)
- C \(\frac{2}{3}\)
- D \(-\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(-\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
\(\int \sin^{-4} x \, \mathrm{d} x = -\cot x - \frac{\cot^3 x}{3}\) \(\left[-\cot x - \frac{\cot^3 x}{3}\right]_{\frac{-\pi}{4}}^{\frac{\pi}{4}} = \left(-\cot\left(\frac{\pi}{4}\right) - \frac{\cot^3\left(\frac{\pi}{4}\right)}{3}\right) - \left(-\cot\left(-\frac{\pi}{4}\right) - \frac{\cot^3\left(-\frac{\pi}{4}\right)}{3}\right)\)
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
- The particular solution of differential equation \((\mathrm{x}+\mathrm{y}) \mathrm{dy}+(\mathrm{x}-\mathrm{y}) \mathrm{d} \mathrm{x}=0\) at \(\mathrm{x}=\mathrm{y}=1\) isMHT CET 2021 Hard
- With usual notations, if in \(\triangle \mathrm{ABC}, 8\) is semi perimeter and \((\mathrm{s}-a)(\mathrm{s}-\mathrm{b})=\mathrm{s}(\mathrm{s}-\mathrm{c})\),
then \(\triangle A B C\) isMHT CET 2020 Medium - A random variable X takes values \(-1,0,1,2\) with probabilities \(\frac{1+3 p}{4}, \frac{1-p}{4}, \frac{1+2 p}{4}, \frac{1-4 p}{4}\) respectively, where p varies over \(\mathbb{R}\). Then the minimum and maximum values of the mean of X are respectively.MHT CET 2024 Hard
- If \(y \sqrt{1-x^{2}}+x \sqrt{1-y^{2}}=1, \quad\) then \(\frac{d y}{d x}=\)MHT CET 2020 Easy
- Let \(A \equiv(0,0), B(3,0), C(0,-4)\) are vertices of \(\triangle A B C\) then the co-ordinates of incentre of \(\triangle A B C\) isMHT CET 2025 Medium
- If \(p: 25\) is an odd prime number.
\(q: 14\) is a composite number and
\(r: 64\) is a perfect square number.
Then which of the following statement pattern is true?MHT CET 2022 Easy
More PYQs from MHT CET
- A radioactive element has a rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it becomes 2500 disintegrations per minute. The decay constant per minute isMHT CET 2017 Medium
- Cross pollination does not occur inMHT CET 2014 Easy
- The amplitude of a particle executing S.H.M. is \(3 \mathrm{~cm}\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy isMHT CET 2023 Medium
- Identify rare earth element from following.MHT CET 2024 Medium
- A polyatomic gas is compressed to \(\left(\frac{1}{8}\right)^{\text {th }}\) of its volume adiabatically.
If its initial pressure is \(P_0\), its new pressure will be \(\left[\right.\) Given, \(\left.\frac{C_p}{C_v}=4 / 3\right]\)MHT CET 2025 Medium - Which among the following polymers restores it's original shape once stretched?MHT CET 2022 Easy