Download App

Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Evaluate: $\int 2^{2^{2^x}} 2^{2^x} 2^x d x$
✓

Answer

(a) : Let $I=\int 2^{2^{2^x}} 2^{2^x} 2^x d x$
Let $2^{2^{2^x}}=t \Rightarrow 2^{2^{2^x}} 2^{2^x} 2^x(\log 2)^3 d x=d t$
$
\Rightarrow I=\int \frac{1}{(\log 2)^3} d t=\frac{1}{(\log 2)^3} t+C=\frac{1}{(\log 2)^3} 2^{2^{2^x}}+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 "M.C.Q (1 Marks)" from Integrals→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 $\text{f(x)}=\begin{cases}\frac{1-\sin^2\text{x}}{3\cos^2\text{x}},&\text{if}\text{ x}<\frac{\pi}{2}\\\text{a},&\text{if}\text{ x}=\frac{\pi}{2}\\\frac{\text{b}(1-\sin\text{x})}{(\pi-2\text{x})^2},&\text{if}\text{ x }>\frac{\pi}{2}\end{cases}$ Then f(x) is continuous at $\text{x}=\frac{\pi}{2},$ if:
  1. $\text{a}=\frac{1}{3},\text{ b}=2$
  2. $\text{a}=\frac{1}{3},\text{ b}=\frac{8}{3}$
  3. $\text{a}=\frac{2}{3},\text{ b}=\frac{8}{3}$
  4. none of these
→
Find the cofactor of each element of the first column of matrix $A=\left[\begin{array}{ccc}2 & 5 & -1 \\ -3 & 0 & 1 \\ 1 & 1 & -1\end{array}\right].$
→
If $f(x) = (ax^2 – b)^3$, then the function $g$ such that $f{g(x)} = g{f(x)}$ is given by:
→
The integrating factor of differential equation $\cos x \frac{d y}{d x}+ y \sin x =1$ is
→
The area of the region bounded by the curve $\text{y}=\sqrt{16-\text{x}^2}\text{ and}\text{ x}-\text{axis}\text{ is:}$
  1. 8p sq. units
  2. 20p sq. units
  3. 16p sq. units
  4. 256p sq. units
→
A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
  1. $\frac{1}{4}$
  2. $\frac{11}{14}$
  3. $\frac{15}{24}$
  4. $\frac{23}{24}$
→
If the direction cosines of a line are $\Big(\frac{1}{\text{c}},\frac{1}{\text{c}},\frac{1}{\text{c}}\Big)$ then:
→
If $y=e^{\frac{1}{2} \log \left(1+\tan ^2 x\right)},$ then $\frac{d y}{d x}$ is equal to
→
If P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear, then R divided PQ in the ratio:
→
Two persons $A$ and $B$ take turns in throwing a pair of dice.The first person to throw $9$ from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins the game is.
→