Questions
If a function is differentiable then for some
is equal to
detailed solution
Correct option is C
Let g(x)=∫0x3 f(t)dt so g(0)=0g′(x)=3x2fx3∫027 f(t)dt=g(3)=g(3)−g(1)3−1+12g(1)−g(0)1−0=g′(α)+12g′(β)for some α∈(1,3),β∈(0,1)⊆(0,3), but g′(α)=3α2fα3and g′(β)=3β2f(β)3Therefore, ∫027 f(t)dt=3α2fα3+12β2fβ3Similar Questions
The value of is
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