help@askiitians.com

1800-150-456-789

Integral Calculus> maximum value...

question mark

find the maximim value of the integral (3/4 -x-X^2)dx lim b to a b is greater than a

pritam samanta , 14 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:

$I = \int_{b}^{a}(\frac{3}{4}-x-x^{2})dx$

$I = (\frac{3x}{4}-\frac{x^{2}}{2}-\frac{x^{3}}{3})_{b}^{a}$

$I = \frac{3(a-b)}{4}-\frac{a^{2}-b^{2}}{2}-\frac{a^{3}-b^{3}}{3}$

$I = \frac{b(4b^{2}+6b-3)-a(4a^{2}+6a-3)}{12}$

$b>a$

$b = a + h, h\geq 0$

$I = \frac{(a+h)(4(a+h)^{2}+6(a+h)-3)-a(4a^{2}+6a-3)}{12}$

$I = \frac{4h^{3} + (12a+6)h^{2} + (12a^{2}+12a-3)h }{12}$

$\frac{\partial I}{\partial h} = \frac{12h^{2} + 2(12a+6)h + (12a^{2}+12a-3) }{12}= 0$

Find ‘h’ from here:

$12h^{2} + 2(12a+6)h + (12a^{2}+12a-3) = 0$

$h = \frac{-2(12a+6)\pm \sqrt{288}}{24}$

$h = -a + \frac{\sqrt{2}-1}{2}$

$b = h +a = \frac{\sqrt{2}-1}{2}$

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

question mark

The area of a square field is 640000cm2.what is its area in hectares

Integral Calculus

1 Answer Available

Last Activity: 2 Year ago(s)

question mark

Please solve this integration. I am facing difficulty in it How to solve this. Please solve anyone. Humble request

Integral Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0

Integral Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

how to solve this?this is interger type question .

Integral Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

Integrate 0 to π/2 (x sin x cos x )/(a²cos²x + b²sin²x)²

Integral Calculus

1 Answer Available

Last Activity: 2 Year ago(s)

View all Questions