Evaluate the following integrals: 9- x^2 dx - Vidyadip

Question

Evaluate the following integrals:
$\int\sqrt{9-{\text{x}^2}}\text{dx}$

✓

Answer

Let $\text{I}=\int\sqrt{3^2-{\text{x}^2}}$
We know that,
$\int\sqrt{\text{a}^2-\text{x}^2}=\frac{\text{x}}{2}\sqrt{\text{a}^2-\text{x}^2}+\frac{\text{a}^2}{2}\sin^{-1}\frac{\text{x}}{\text{a}}+\text{C}$
$\therefore\ \text{I}=\frac{\text{x}}{2}\sqrt{9-\text{x}^2}+\frac{9}{2}\sin^{-1}\frac{\text{x}}{3}+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Indefinite Integrals→Indefinite Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $y=3 \cos x-2 \sin x$, then prove that $\frac{d^2 y}{d x^2}-y=0$

Find the second order derivatives of the following functions:
$\text{y}=\text{x}^3\log\text{x}$

Four cards are drawn simultaneously from a well shuffled pack of 52 playing cards. Find the probability distribution of the number of aces.

Find the integrals of the functions in Exercises:
$\frac{\sin^2\text{x}}{1+\cos\text{x}}$

Write a value of $\int\log_\text{e}\text{x}\text{ dx}$

Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=3+(\text{x}-2)^{\frac{2}{3}}\text{ on }[1,3]$

Using Rolle's theorem, find points on the curve $\text{y}=16-\text{x}^2,\text{x}\in[-1,1],$ where tagent is parallel to $x-$axis.

Evaluate the following integrals:
$\int (3\text{x}\sqrt{\text{x}}+4\sqrt{\text{x}}+5)\text{dx}$

Find the adjoint of the following matrices:$\begin{bmatrix}-3 & 5 \\ 2 & 4 \end{bmatrix}$
Verify that (adjoint A) A = |A|I = A (adjoint A) for the above matrices.

Differentiate the following functions with respect to x:
$\tan5\text{x}^\circ$