AP EAMCET · Maths · Definite Integration
The value of \(f(\mathrm{l})\), given the equation \(\int_0^{x^2} x f(t) d t=x^5-x^3\) is
- A 4
- B 3
- C 2
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\(\int_0^{x^2} x \cdot f(t) d t=x^5-x^3\) Differentiate w.r.t. \(x\) on both sides, \[ \begin{aligned} x^2 \cdot f\left(x^2\right) \cdot \frac{d}{d x} x^2-0 & =5 x^4-3 x^2 \\ x^2 f\left(x^2\right)(2 x) & =5 x^4-3 x^2 \end{aligned} \] \[ 2 x^3 f\left(x^2\right)=5 x^4-3 x^2 \] Put…
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
- If and are all distinct, thenAP EAMCET 2021 Medium
- \(\int \frac{1-\cos x}{\cos x(1+\cos x)} d x=\)AP EAMCET 2023 Medium
- The distance between the lines represented by \(4 x^2+20 x y+25 y^2+2 x+5 y-12=0\) is equal toAP EAMCET 2022 Medium
- The number of integral vaules of \(x\) satisfying \(5 x-1 < (x+1)^2 < 7 x-3\) isAP EAMCET 2018 Hard
- The equation of the line, passing through the point \(\left(a \cos ^3 \theta, a \sin ^3 \theta\right)\) and perpendicular to the line \(x \cos\) \(\theta-y \sin \theta=a\), isAP EAMCET 2023 Easy
- The position vectors of \(P\) and \(Q\) are respectively \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\). If \(\mathrm{R}\) is a point on \(\overrightarrow{\mathrm{PQ}}\) such that \(\overrightarrow{\mathrm{PR}}=5 \overrightarrow{\mathrm{PQ}}\), then the position vector of \(R\) isAP EAMCET 2008 Medium
More PYQs from AP EAMCET
- If \(\sin (2 x)=\frac{\sqrt{5}-1}{4}\) then \(x=\frac{n}{2} \pi+(-1)^n(m)\), \(n \in \mathbf{Z}\), find \(m\).AP EAMCET 2020 Easy
- Reduction of a metal oxide in liquid state is easier than in the solid state becauseAP EAMCET 2017 Easy
- In Lassaigne's test for halogens, it is necessary to remove and from the sodium fusion extract, if nitrogen and Sulphur are present. This is done by boiling the extract with . Identify and .AP EAMCET 2021 Medium
- If a ball projected vertically upwards with certain intitial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s, then the initial velocity of the ball is
(Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )AP EAMCET 2025 Medium - The half life of a stream of radioactive particles moving along a straight path with a constant kinetic energy of \(4 \mathrm{eV}\) is 1 minute. The percentage of particles which decay before travelling a distance of \(3.6 \mathrm{~km}\) is (Mass of the radioactive particles \(=3.2 \times 10^{-21} \mathrm{~kg}\) and charge of the electron \(=1.6 \times 10^{-19} \mathrm{C}\) ).AP EAMCET 2017 Medium
- If the vectors \(\mathbf{A B}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\), \(\mathbf{A C}=5 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two sides of a triangle \(A B C\), whose centroid is \(G\), then \(|\mathbf{A G}|=\)AP EAMCET 2019 Hard