help@askiitians.com

1800-150-456-789

Differential Calculus> Image attached ….....

question mark

Image attached ….....

milind , 10 Years ago

Grade 12

2 Answers

Jitender Singh

Last Activity: 10 Years ago

Hello student,
Please find answer to your question
$I_{n} = \frac{d^{n}}{dx^{n}}(x^{n}log(x))$
$I_{1} = \frac{d}{dx}(xlog(x))$
$I_{1} = 1 + log(x)$
$I_{2} = \frac{d^{2}}{dx^{2}}(x^{2}log(x))$
$I_{2} = 3 + 2log(x)$
$I_{3} = \frac{d^{3}}{dx^{3}}(x^{3}log(x))$
$I_{3} = 11 + 6log(x)$
$I_{4} = \frac{d^{4}}{dx^{4}}(x^{4}log(x))$
$I_{4} = 50 + 24log(x)$
$I_{5} = \frac{d^{5}}{dx^{5}}(x^{5}log(x))$
$I_{5} = 274 + 120log(x)$
$I_{5}-5I_{4} = 24 = 4! = (5-1)!$
$I_{4}-4I_{3} = 6 = 3! = (4-1)!$
$I_{3}-3I_{2} = 2 = 2! = (3-1)!$
Similarly, you can prove for n,
$I_{n}-nI_{n-1} = (n-1)!$

milind

Last Activity: 10 Years ago

Sir explain this solution. I_{n =}d^n-1/dx^n-1[x^n-1 + nx^n-1 log x ] In = (n-1) d^n-2/ dx ^n-2x^n-2+ n d^n-1/ dx^n-1(x^n-1logx)

I_{n =}(n-1 ) ! + nI_n-1

In – nI_n-1=(n-1)! Proved

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 diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution tomove once over to level a playground. find the area of the playground in square m?

Differential Calculus

1 Answer Available

Last Activity: 1 Year ago(s)

question mark

Find dy/DX when y=x^sinx+sin-1√x. Please give me the solution of this problem.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin Cwhere A + B + C = T(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

Differential Calculus

0 Answer Available

Last Activity: 2 Year ago(s)

View all Questions