AP EAMCET · Maths · Indefinite Integration
\(\int_0^k(\sqrt{k}-\sqrt{t})^2 d t=\)
- A \(\frac{k^2}{2}\)
- B \(\frac{k^2}{4}\)
- C \(\frac{k^2}{6}\)
- D \(\frac{k^2}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{k^2}{6}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \int_0^k(\sqrt{k}-\sqrt{t}) d t & =\int_0^k(k+t-2 \sqrt{k} \sqrt{t}) d t \\ & =\left(k t+\frac{t^2}{2}\right)_0^k-2 \sqrt{k}\left(\frac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}\right)_0^k \\ & =\left(k \cdot k+\frac{k^2}{2}\right)-\frac{4…
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
- \(\int \operatorname{Cos}^{-1}\left(2 x^2-1\right) d x=\)AP EAMCET 2017 Hard
- \(\cos \alpha \sin (\beta-\gamma)+\cos \beta \sin (\gamma-\alpha)\) \(+\cos \gamma \sin (\alpha-\beta)\) is equal toAP EAMCET 2003 Medium
- If \(f: R \rightarrow R\) defined by
\[
f(x)=\left\{\begin{array}{cc}
a^2 \cos ^2 x+b^2 \sin ^2 x, & x \leq 0 \\
e^{a x+b}, & x>0
\end{array}\right.
\]
is a continuous function, thenAP EAMCET 2002 Hard - If \(I_n=\int_0^{\pi / 4} \tan ^n \theta d \theta\) for \(n=1,2,3, \ldots\), then \(I_{n-1}+I_{n+1}\) is equal toAP EAMCET 2011 Hard
- \(\lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x}{\sin ^2 x}=\)AP EAMCET 2024 Medium
- Events \(A, B\) and \(C\) are mutually exclusive events such that \(P(A)=\frac{3 x+1}{3}, P(B)=\frac{1-x}{4}\) and \(P(C)=\frac{1-2 x}{2}\). The set of possible values of \(x\) are in the intervalAP EAMCET 2021 Hard
More PYQs from AP EAMCET
- The four distinct points \((0,0),(2,0),(0,-2)\) and \((k,-2)\) are concyclic, if \(k\) is equal toAP EAMCET 2002 Easy
- By simplifying \(i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}\), we getAP EAMCET 2022 Easy
- Arrange the following in the increasing order of their magnetic moments
I. \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}\)
II. \(\left[\mathrm{Mn} \mathrm{Cl}_6\right]^{3-}\)
III. \(\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}\)
IV. \(\left[\mathrm{FeF}_6\right]^{3-}\)AP EAMCET 2024 Medium - While solving a system of linear equations \(\mathrm{AX}=\mathrm{B}\) using Cramer's rule with the usual notation if
\(\Delta=\left|\begin{array}{ccc}1 & 1 & 1 \\ 2 & -1 & 2 \\ -1 & 1 & 5\end{array}\right| ; \Delta_1=\left|\begin{array}{ccc}5 & 1 & 1 \\ 4 & -1 & 2 \\ 11 & 1 & 5\end{array}\right|\) and \(X=\left[\begin{array}{l}\alpha \\ 2 \\ \beta\end{array}\right]\) then
\(\alpha^2+\beta^2=\)AP EAMCET 2024 Easy - The common name of isopropyl benzene isAP EAMCET 2020 Easy
- A police party is moving in a jeep at a constant speed \(v\). They saw a thief at a distance \(x\) on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration \(a\). Which of the following relations is true if the police is able to catch the thief?AP EAMCET 2011 Hard