Evaluate the following integrals: 4+ ^2x dx - Vidyadip

Question

Evaluate the following integrals:$\int\frac{\cos\text{x}}{\sqrt{4+\sin^2\text{x}}}\text{ dx}$

✓

Answer

$\int\frac{\cos\text{x}\text{ dx}}{\sqrt{4+\sin^2\text{x}}}$ Let $\sin\text{x}=\text{t}$ $\Rightarrow\cos\text{x}\text{ dx}=\text{dt}$ Now, $\int\frac{\cos\text{x}\text{ dx}}{\sqrt{4+\sin^2\text{x}}}$$=\int\frac{\text{dt}}{\sqrt{2^2-\text{t}^2}}$
$=\log\Big|\text{t}+\sqrt{4+\text{t}^2}\Big|+\text{C}$$=\log\Big|\sin\text{x}+\sqrt{4+\sin^2\text{x}}\Big|+\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 "Solve the Following Question.(3 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Differentiate the following w. r. t. x.$\cot ^{-1}\left(\frac{\cos x}{1+\sin x}\right)$

Express the following equations in matrix form and solve them by the method of reduction: $x+y+z=6,3 x-y+3 z=6$ and $5 x+5 y-4 z=3$.

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

The probability that certain kind of component will survive a check test is $0.6.$ Find the probability that exactly $2$ of the next $4$ tested components survive

The surface area of a spherical balloon is increasing at the rate of 2 cm2/sec. At what rate is the volume of the balloon is increasing, when the radius of the balloon is 6 cm?

Evaluate the following :

$\int \sqrt{\frac{10+x}{10-x}} \cdot d x$

Evaluate the following intregals:
$\int\frac{1}{(\text{x}-1)(\text{x}+1)(\text{x}+2)}\ \text{dx}$

If $\sec ^{-1}\left(\frac{x+y}{x-y}\right)=a^2$, show that $\frac{d y}{d x}=\frac{y}{x}$

Evaluate the following intregals:
$\int\frac{\text{x}}{\sqrt{\text{x}^2+\text{x}+1}}\text{dx}$

Find the equation of the tangent to the curve $\sqrt{\text{x}}+\sqrt{\text{y}}=\text{a},$ at the point $\Big(\frac{\text{a}^2}{4},\frac{\text{a}^2}{4}\Big).$