Evaluate \( \int \frac{\left(\sqrt[3]{x+\sqrt{2-x^{2}}}\right)\left(\sqrt[6]{1-x \sqrt{2-x^{2}}}...

Channel:
PW Solutions
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=5JBOIdPnkUE


Duration: 6:48
0 views
0

Evaluate \( \int \frac{\left(\sqrt[3]{x+\sqrt{2-x^{2}}}\right)\left(\sqrt[6]{1-x \sqrt{2-x^{2}}}\right) d x}{\sqrt[3]{1-x^{2}}} ; x \in(0,1) \)
(a) \( 2^{\frac{1}{6}} x+C \)
(b) \( 2^{\frac{1}{12}} x+C \)
(c) \( 2^{\frac{1}{3}} x+C \)
(d) \( 2^{\frac{1}{9}} x+C \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-09Evaluate: \( \int \sqrt{\frac{5-x}{x-2}} d x \)
2023-06-09Evaluate: \( \int \tan ^{-1}(\sec x+\tan x) \cdot d x \) is
2023-06-09Evaluate: \( \int \frac{2 e^{5 x}+e^{4 x}-4 e^{3 x}+4 e^{2 x}+2 e^{x}}{\left(e^{2 x}+4\right)\le...
2023-06-09Evaluate: \( I=\int \frac{(\cos 2 x-3) d x}{\cos ^{4} x \sqrt{4-\cot ^{2} x}} \)
2023-06-09Evaluate: \( \int \frac{x d x}{\left(1+x^{2}+\sqrt{\left(1+x^{2}\right)^{3}}\right.} \)
2023-06-09Evaluate: \( \int x \cdot \sqrt{\frac{2 \sin \left(x^{2}+1\right)-\sin 2\left(x^{2}+1\right)}{2 ...
2023-06-09Evaluate \( \int \frac{\sqrt{x-1}}{x \sqrt{x+1}} d x \) (a) \( \ln \left(x+\sqrt{x^{2}-1}\right)...
2023-06-09Evaluate: \( \int \tan 3 x \tan 2 x \tan x d x \)
2023-06-09Let \[ \begin{array}{l} \int \frac{f^{\prime}(x) g(x)-g^{\prime}(x) f(x)}{(f(x)+g(x)) \sqrt{f(x)...
2023-06-09Prove that: (i) \( \int 1 / \sqrt{\left(1-x^{2}\right)} \cdot d x=\sin ^{-1} x+C \) (ii) \( \int...
2023-06-09Evaluate \( \int \frac{\left(\sqrt[3]{x+\sqrt{2-x^{2}}}\right)\left(\sqrt[6]{1-x \sqrt{2-x^{2}}}...
2023-06-09\[ \int \frac{x^{3}-1}{\left(x^{4}+1\right)(x+1)} d x \] (a) \( \frac{1}{4} \ln \left(1+x^{4}\ri...
2023-06-09\[ \int \sqrt{\frac{(2023)^{2 x}}{1-(2023)^{2 x}}}(2023)^{\sin ^{-1}(2023)^{x}} d x= \] (a) \( \...
2023-06-09\( \int \frac{3 x^{2}+4 x-1}{\left(x^{2}+1\right)^{2} \sqrt{x+1}} d x \) is equal to: (a) \( \fr...
2023-06-09A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index ...
2023-06-09\( \int \frac{\cos ^{2} x-x^{2} \sin x}{(x+\cos x)^{2}} d x \) is equal to (a) \( \frac{x \cos x...
2023-06-09Let \( A=\left[\begin{array}{ccc}x^{2} & 6 & 0 \\ 1 & -5 & 1 \\ 2 & 0 & x\end{array}\right] \) a...
2023-06-09In free space, an electromagnetic wave of \( 3 \mathrm{GHz} \) strikes over the edge of an objec...
2023-06-09\( \int \frac{x^{2}}{(a+b x)^{2}} d x \) equals (a) \( \frac{1}{b^{3}}\left(a+b x-a \ln |a+b x|-...
2023-06-09Let \( f(x)=\int \frac{x^{2} d x}{\left(1+x^{2}\right)\left(1+\sqrt{1+x^{2}}\right)} \) and \( f...
2023-06-09The value of \( \int \frac{(\cos 2 x)^{2}}{\sin x} d x \) (a) \[ \begin{array}{l} -\ln \left[\co...