TS EAMCET · Maths · Definite Integration
\(\int_{-5}^5 x^4\left(25-x^2\right)^{5 / 2} d x=\)
- A \(\frac{5^9}{2} \frac{\pi}{2}\)
- B \(\frac{16\left(5^9\right)}{63}\)
- C \(\frac{3\left(5^{10}\right)}{256} \pi\)
- D \(\frac{16\left(5^{10}\right)}{693}\)
Answer & Solution
Correct Answer
(C) \(\frac{3\left(5^{10}\right)}{256} \pi\)
Step-by-step Solution
Detailed explanation
Let \(\begin{aligned} l & =\int_{-5}^5 x^4\left(25-x^2\right)^{5 / 2} d x \\ & =2 \int_0^5 x^4\left(25-x^2\right)^{5 / 2} d x\end{aligned}\) Put, \(x=5 \sin \theta \Rightarrow d x=5 \cos \theta d \theta\)…
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 normal at a point on the parabola \(y^2=4 x\) passes through \((5,0)\). If there are two more normals to this parabola which pass through \((5,0)\), the centroid of the triangle formed by the feet of these three normals isTS EAMCET 2020 Medium
- The shortest distance between the lines \(\overline{\mathrm{r}}=(3 \bar{i}-5 \bar{j}+2 \bar{k})+t(4 \bar{i}+3 \bar{j}-\bar{k})\) and \(\overline{\mathrm{r}}=(\bar{i}+2 \bar{j}-4 \bar{k})+s(6 \bar{i}+3 \bar{j}-2 \bar{k})\) isTS EAMCET 2025 Medium
- unbiased coins are tossed. The probability of having the number of heads is not equal to the number of tails isTS EAMCET 2020 Medium
- If , then determinant ofTS EAMCET 2021 Easy
- The angle between the pair of straight lines isTS EAMCET 2021 Easy
- If 4 letters are selected at random from the letters of the word PROBABILITY, then the probability of getting a combination of letters in which atleast one letter is repeated isTS EAMCET 2024 Medium
More PYQs from TS EAMCET
- Different material of two identical long bars \(A\) and \(B\) are coated with wax and have their one end immersed in a hot oil bath. When the steady state is reached, the lengths for which wax melt are \(l_A\) and \(l_B\). If \(k_A\) and \(k_B\) are thermal conductivities of materials, thenTS EAMCET 2020 Easy
- If thenTS EAMCET 2022 Medium
- \(P\) is a \(3 \times 3\) square matrix and \(\operatorname{Tr}(P) \neq 0\). If \(\operatorname{Tr}\left(\mathrm{P}-\mathrm{P}^{\mathrm{T}}\right)+\operatorname{Tr}\left(\mathrm{P}+\mathrm{P}^{\mathrm{T}}\right)+\frac{\operatorname{Tr}(P)}{\operatorname{Tr}\left(P^T\right)}+\operatorname{Tr}(\mathrm{P}) \times \operatorname{Tr}\left(\mathrm{P}^{\mathrm{T}}\right)=\) 0 then \(\operatorname{Tr}(\mathrm{P})=\)TS EAMCET 2023 Medium
- \(\cos \alpha \sin (\beta-\gamma)+\cos \beta \sin (\gamma-\alpha)\) \(+\cos \gamma \sin (\alpha-\beta)\) is equal toTS EAMCET 2003 Medium
- If \(A+B+C=\frac{\pi}{3}\) then \(\sin \left(\frac{\pi-6 A}{6}\right)+\sin \left(\frac{\pi-6 B}{6}\right)+\sin C=\)TS EAMCET 2019 Hard
- One litre of oxygen at a pressure of \(1 \mathrm{~atm}\) and two litres of nitrogen at a pressure of \(0.5 \mathrm{~atm}\), are introduced into a vessel of volume \(1 \mathrm{~L}\). If there is no change in temperature, the final pressure of the mixture of gas (in atm) isTS EAMCET 2008 Hard