^2(2x+5)dx - Vidyadip

Question

$\int\sin^2(2\text{x}+5)\text{dx}$

✓

Answer

$\int\sin^2(2\text{x}+5)\text{dx}$
$=\int\Big(\frac{1-\cos(4\text{x}+10)}{2}\Big)\text{dx}$ $\Big[\therefore\sin^2\text{A}=\frac{1-\cos2\text{A}}{2}\Big]$
$=\frac{1}{2}\int(1-\cos(4\text{x}+10))\text{dx}$
$=\frac{1}{2}\Big[\text{x}-\frac{\sin(4\text{x}+10)}{4}\Big]+\text{C}$
$=\frac{1}{2}\text{x}-\frac{\sin(4\text{x}+10)}{8}+\text{C}$

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 "2 Marks Questions" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int\frac{\text{e}^{\sqrt{\text{x}}}\cos\big(\text{e}^{\sqrt{\text{x}}}\big)}{\sqrt{\text{x}}}\text{ dx}$

Evaluate the following integrals:
$\int\limits^{4}_2\frac{\text{x}}{\text{x}^2+1}\text{dx}$

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that.
First ball is black and second is red.

$\int\sin^2\text{bx dx}$

If $\text{x}=\text{f}(\text{t})$ and $\text{y}=\text{g}(\text{t}),$ then write the value of $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$

Integrate the rational function $\frac{3 x-1}{(x+2)^{2}}$

If A and B are independent events, then write expression for P(exactly one of A, B occurs).

If $\tan^{-1}\big(\sqrt{3}\big)+\cot^{-1}\text{x}=\frac{\pi}{2},$ find x.

Find $x, y, z$ in $\left[\begin{array}{cc}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$

Find the local maxima and local minima, of function. Find also the local maximum and the local minimum value, as the case may be: $f(x) = x^2$