Question
Evaluate :
$\int_0^{\frac{1}{\sqrt{2}}} \frac{\sin ^{-1} x}{\left(1-x^2\right)^{\frac{3}{2}}} \cdot d x$
✓
Answer
Get the step-by-step solution for this question inside the Vidyadip app.
Get the answer in the appNeed a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Obtain the equation of the plane passing through the point (1, - 3, -2) and perpendicular to the planes x + 2y + 2z = 5 and 3x + 3y + 2z = 8.
Find the equation of the tangent to the curve $\sqrt{\text{x}}+\sqrt{\text{y}}=\text{a},$ at the point $\Big(\frac{\text{a}^2}{4},\frac{\text{a}^2}{4}\Big).$
→Evaluate the following integrals:$\int\tan^{-1}\Big(\frac{3\text{x}-\text{x}^3}{1-3\text{x}^2}\Big)\text{dx}$
→If $\mathrm{D}, \mathrm{E}, \mathrm{F}$ are the mid-points of the sides $\mathrm{BC}, \mathrm{CA}, \mathrm{AB}$ of a triangle $\mathrm{ABC}$, prove that $\overline{A D}+$
→$\overline{B E}+\overline{C F}=0$
Evaluate the following integrals:$\int\frac{\text{x}+5}{3\text{x}^2+13\text{x}-10}\text{ dx}$
→Find the principal solutions of the following equations : tanθ = -1
If $\text{x}=\text{a}\cos\text{nt}-\text{b}\sin\text{nt}$ and $\frac{\text{d}^2\text{x}}{\text{dt}^2}=\lambda\text{x}$ then find the value of $\lambda.$
→The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is $\frac{28\times9^6}{10^8}$.
→Diffrentiate the following w. r. t. x.
→$\cos ^{-1}\left(\frac{3 \cos \left(e^x\right)+2 \sin \left(e^x\right)}{\sqrt{13}}\right)$
If $f^{\prime}(x)=k(\cos x-\sin x), f^{\ \prime}(0)=3$ and $f\left(\frac{\pi}{2}\right)=15$, find $f(x)$
→