Tags Application of Integrals

Application of Integrals

Get insights from 41 questions on Application of Integrals, answered by students, alumni, and experts. You may also ask and answer any question you like about Application of Integrals

Follow Ask Question

Questions

Discussions

Active Users

Followers

New answer posted

5 months ago

Application of Integrals Class 12th

9. Find the area of the region bounded by the parabola y = x² and y = |x|

0 Follower 4 Views

Vishal Baghel

Contributor-Level 10

Given that equation of

curve $y = x^{2}$

line $y = | x | = {x, i f x \geq 0 & - x, i f x ∠ 0}$

Since the line passes through A&B in Ist and IInd quadrants

the equation must satisfy

$\Rightarrow y = x^{2}$

$\Rightarrow x = x^{2}$ for Ist quadrant and

$\Rightarrow - x = x^{2}$ for IInd t quadrant

So, $\Rightarrow x^{2} - x = 0$ and $x^{2} + x = 0$

$\Rightarrow x (x - 1) = 0$ and $x (x + 1) = 0$

$\Rightarrow x = 0, 1$ $x = 0, - 1$

$x = 0, y = 0$

$x = 1, y = 1$ i.e, A has coordinate (1,1)

$x = - 1, y = 1$ i.e, B has coordinate (1,1)

Now, area of AODA = area (AOM)-area (ADOM)

$= \int_{0}^{1} y_{l i n e} d x - \int_{0}^{1} y_{c u r v e} d x$

$= \int_{0}^{1} x d x - \int_{0}^{1} x^{2} d x = {[\frac{x^{2}}{2}]}_{0}^{1} - {[\frac{a^{3}}{3}]}_{0}^{1}$

$= \frac{1}{2} - \frac{1}{3} = \frac{3 - 2}{6} = \frac{1}{6} u n i t s^{2}$

$∴$ The required area of the region bounded by curve $y = x^{2}$ and line $y = | x |$ is $\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} u n i t s^{2}$

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

8. The area between x = y² and x = 4 is divided into two equal parts by the line x = a find the value of a

0 Follower 7 Views

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

\begin{array}{l} \Rightarrow {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{0}^{a} = {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{a}^{} \\ \Rightarrow \frac{2}{3} [a^{\frac{3}{2}} - 0] = \frac{2}{3} [4^{\frac{3}{2}} - a^{\frac{3}{2}}] \\ \Rightarrow a^{\frac{3}{2}} = 4^{\frac{3}{2}} - a^{\frac{3}{2}} \\ \Rightarrow 2 a^{\frac{3}{2}} = 4^{\frac{3}{2}} \end{array}

$\Rightarrow 4 a^{3} = 4^{3}$ (Squaring both sides)

$\Rightarrow a^{3} = 4^{2}$

$\Rightarrow a = 4^{\frac{2}{3}}$ (Taking cube on both sides)

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

7. Find the area of the smaller part of the circle x² + y² = a² cut off by the line x = a/√2

0 Follower 1 View

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

New question posted

5 months ago

Application of Integrals Class 12th

7. Find the area of the smaller part of the circle x² + y² = a² cut off by the line x = a/√2

0 Follower 7 Views

New answer posted

5 months ago

Application of Integrals Class 12th

6. Find the area of the region in the first quadrant enclosed by x-axis,line $x = \sqrt3y$ and the circle $x^{2} + y^{2} = 4$ .

0 Follower 2 Views

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

5. Find the area of the region bounded by the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

0 Follower 1 View

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

4. Find the area of the region bounded by the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ .

0 Follower 1 View

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

3. Find the area of the region bounded by the curve x² = 4y ,y=2,y=4 and y-axis is the first quadrant.

0 Follower 7 Views

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

2. Find the area of the region bounded by the curve y² = 9x and the lines x=2,x=4 and x-axis in the first quadrant.

0 Follower 2 Views

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

New answer posted

5 months ago

Application of Integrals Class 12th

1. Find the area of the region bounded by the curve y² = x the lines x=1, x = 4 and x-axis.

0 Follower 8 Views

Vishal Baghel

Contributor-Level 10

Kindly go through the solution

0 0

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
679k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Need guidance on career and education? Ask our experts

Your Question

Application of Integrals

Questions

Discussions

Active Users

Followers

All

Discussions

Unanswered Questions

Share Your College Life Experience