If y= _ u(x) ^ v(x) f(t) d t let us define d y d x in a different manner as d y d x =v^…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
If \[y=\int_{u(x)}^{v(x)} f(t) d t\] let us define \(\frac{d y}{d x}\)in a different manner
as \(\frac{d y}{d x}=v^{\prime}(x) f^{2}(v(x))-u^{\prime}(x) f^{2}(u(x))\)and the equation of the tangent at
as \(y-b=\left(\frac{d y}{d x}\right)_{(a, b)}(x-a)\)
If F (x) \(=\int_{1}^{\mathrm{x}} \mathrm{e}^{\mathrm{t}^{2} / 2}\)(1 – t2) dt, then \(\frac{\mathrm{d}}{\mathrm{dx}}\) F (x) at x = 1 is
- 0
- 1
- 2
- –1
Answer
(A) 0
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