Integral Limits

Calculus Level 3

Given that F ( x ) = ∫ 0 x f ( t ) d t \displaystyle F(x) = \int_0^x f(t) \, dt , and F ( x 2 ) = x 3 + 3 x 2 F(x^2) = x^3 + 3x^2 , find f ( 4 ) f(4) .

-3 7 4 6

Ayush Bhardwaj by Ayush Bhardwaj , 22, India

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2 solutions

Ayush Bhardwaj
Jan 29, 2016

F'(x)=d(∫ f(t)dt)/dx
=f(x).d(x)/dx - 0 =f(x) [Newton Leibnitz Theorum]
=>F'(x)=f(x) ..........1)

F(x^2)= x^3 + 3x^2
[DIfferientiate with respect to x]
F'(x^2).2x = 3x^2 + 6x
F'(x^2) = 3x/2 + 3
F'(x) = 3(root(x))/2 + 3
=>f(4) = 3 + 3 = 6 [Answer]

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Subh Mandal
Sep 7, 2016

Chutiye question kyu daal raha hai madarchod.

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Date dekhle kab dala tha.

Ayush Bhardwaj - 4 years, 9 months ago

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