For \( a0 \), if \( I=\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=A \sin ^{-1}\left(\frac{x^{3 / 2}}{B...

Channel:
PW Solutions
Subscribers:
453,000
Published on ● Video Link: https://www.youtube.com/watch?v=jcLDhcrRcM4


Duration: 4:40
1 views
0

For \( a0 \), if \( I=\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=A \sin ^{-1}\left(\frac{x^{3 / 2}}{B}\right)+C \), where \( C \) is any arbitrary constant, then :
(a) \( A=\frac{2}{3} \)
(b) \( B=a^{3 / 2} \)
(c) \( A=\frac{1}{3} \)
(d) \( B=a^{1 / 2} \)
šŸ“²PW App Link - https://bit.ly/YTAI_PWAP
šŸŒPW Website - https://www.pw.live



Other Videos By PW Solutions


2022-10-28The solution of differential equation \( \frac{d^{2} y}{d x^{2}}=\frac{d y}{d x}, y(0)=3 \) and ...
2022-10-28Let \( I=\int_{0}^{\pi} x^{6}(\pi-x)^{8} d x \), then \( \frac{\pi^{15}}{\left({ }^{15} C_{9}\ri...
2022-10-28let \( f(x)=\int_{0}^{x} e^{x-y} f^{\prime}(y) d y-\left(x^{2}-x+1\right) e^{x} \) Find the numb...
2022-10-28If \( \int_{a}^{b}|\sin x| d x=8 \) and \( \int_{0}^{a+b}|\cos x| d x=9 \) then the value of \( ...
2022-10-28If \( \int \frac{d x}{\cos ^{3} x-\sin ^{3} x}=A \tan ^{-1}(f(x))+B \ln \left|\frac{\sqrt{2}+f(x...
2022-10-28If \( \int \frac{d x}{x^{4}\left(1+x^{3}\right)^{2}}=a \ln \left|\frac{1+x^{3}}{x^{3}}\right|+\f...
2022-10-28If maximum value of \( \int_{0}^{1}(f(x))^{3} d x \) under the condition \( -1 \leq f(x) \leq 1 ...
2022-10-28The value of \( \int \frac{\tan x}{\tan ^{2} x+\tan x+1} d x=x-\frac{2}{\sqrt{A}} \tan ^{-1}\lef...
2022-10-28Let \( f: R \rightarrow\left[\frac{3}{4}, \infty\right) \) be a surjective quadratic function wi...
2022-10-28Let \( g(x)=x^{C} e^{C x} \) and \( f(x)=\int_{0}^{x} t e^{2 t}\left(1+3 t^{2}\right)^{1 / 2} d ...
2022-10-28For \( a0 \), if \( I=\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=A \sin ^{-1}\left(\frac{x^{3 / 2}}{B...
2022-10-28The value of the definite integral \( \int_{-1}^{1} e^{-x^{4}}\left(2+\ln \left(x+\sqrt{x^{2}+1}...
2022-10-28If \( f(x) \) is a continuous function for all real values of \( x \) and satisfies \( \int_{n}^...
2022-10-28Consider the function \( f(x)=\frac{\ln x}{8}-a x+x^{2} \) and \( a \geq 0 \) is a real constant :
2022-10-28If \( \int_{0}^{1} e^{-x^{2}} d x=a \), then \( \int_{0}^{1} x^{2} e^{-x^{2}} d x \) is equal to...
2022-10-28Let \( f(x)=1+\int_{0}^{1}\left(x e^{y}+y e^{x}\right) f(y) d y \) where \( x \) and \( y \) are...
2022-10-28Which of the following is suitable for experiments on linkage? (a) AABB \( \times \) aabb (b) \(...
2022-10-28Even in absence of pollinating agents seed setting is assured in (a) Commelina (b) Zostera (c) S...
2022-10-28The following table shows the genotypes for \( A B O \) blood grouping and their phenotypes. In ...
2022-10-28A mutation is a (a) sudden temporary change in an organism's genetic material. (b) change in phe...
2022-10-28A simplified representation of nitrogen cycle is given here. Which of the following statements r...


Tags:
pw