Download App

Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Evaluate: $\int \frac{\left(x^4-x\right)^{\frac{1}{4}}}{x^5} d x$
✓

Answer

(a) : Let $I=\int \frac{\left(x^4-x\right)^{\frac{1}{4}}}{x^5} d x$
$
\Rightarrow \quad I=\int \frac{x\left(1-\frac{1}{x^3}\right)^{\frac{1}{4}}}{x^5} d x=\int \frac{\left(1-\frac{1}{x^3}\right)^{\frac{1}{4}}}{x^4} d x
$
Put $1-\frac{1}{x^3}=t \Rightarrow \frac{3}{x^4} d x=d t$

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

A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is,
→
If  m[-3, 4] + n[4, -3] = [10, -11] then 3m + 7n = 3m + 7n =
  1. 3
  2. 5
  3. 10
  4. 1
→
$\int\frac{\text{x}^9}{(4\text{x}^2+1)^6}\text{dx}$  is equal to:
  1. $\frac{1}{5\text{x}}\Big(4+\frac{1}{\text{x}^2}\Big)^{-5}+\text{c}$
  2. $\frac{1}{5}\Big(4+\frac{1}{\text{x}^2}\Big)^{-5}+\text{c}$
  3. $\frac{1}{10\text{x}}\Big(\frac{1}{\text{x}}+4\Big)^{-5}+\text{c}$
  4. $\frac{1}{10\text{x}}\Big(\frac{1}{\text{x}^2}+4\Big)^{-5}+\text{c}$
→
For a linear programming equations, convex set of equations is included in region of:
→
If $A$ is an invertible matrix, then det $(A^{-1})$ is equal to$:$
→
A rectangular parallelopiped is formed by planes drawn through the point (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is:
  1. 2
  2. 3
  3. 4
  4. all of these
→
Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is:
  1. Neither reflexive nor transitive.
  2. Neither symmetric nor transitive.
  3. Transitive.
  4. None of these.
→
A and B are two points and C is any point collinear with A and B. IF AB=10, BC=5, then AC is equal to:
  1. either 15 or 5
  2. necessarily 5
  3. necessarily 16
  4. none of these
→
The vector equation of the plane containing the line $\vec{\text{r}}=(-2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}})+\lambda(3\hat{\text{i}}-2\hat{\text{j}}-\hat{\text{k}})$ and the point $\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ is:
  1. $\vec{\text{r}}.(\hat{\text{i}}+3\hat{\text{k}})=10$
  2. $\vec{\text{r}}.(\hat{\text{i}}-3\hat{\text{k}})=10$
  3. $\vec{\text{r}}.(3\hat{\text{i}}+\hat{\text{k}})=10$
  4. $\text{None of these}$
→
Choose the correct answer from the given four options.
The plane 2x – 3y + 6z – 11 = 0 makes an angle $\sin^{-1}(\alpha)$ with x-axis. The value of $\alpha$ is equal to:
→