Question

Let F(x)=integral 0 to x^2 f(t)dt if F(x)=x^2(1+x) them f(4)=

Answer 1

by using Leibniz

F'(x) = 2x f(x²) ....(1)

according to question

F(x) = x²(1+x)

so

F'(x) = 2x + 3x² .....(2)

now put value of F'(x) in equation. (1)

2x+3x² = 2x f(x²)

now put x =2

2×2 +3×2² = 2×2×f(4)

4+12 = 4f(4)

f(4) = 16/4

f(4) = 4

hope it can help you ✌✌✌...