2 votes 2 votes Let $f$ be a continuous function with $f(1) = 1$. Define $$F(t)=\int_{t}^{t^2}f(x)dx$$. The value of $F’(1)$ is $-2$ $-1$ $1$ $2$ Calculus isi2018-mma engineering-mathematics calculus integration + – akash.dinkar12 asked May 11, 2019 akash.dinkar12 1.1k views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments srestha commented May 12, 2019 reply Follow Share I cannot remember now. But I think $f(x)=e^{x}$ Now, integration putting upper bound $\int e^{t^{2}}dt$ is it not form of laplace? 0 votes 0 votes slow_but_detemined commented Jan 27, 2020 reply Follow Share Its just differentiation with respect to the limit of integration. https://math.stackexchange.com/questions/984111/differentiating-with-respect-to-the-limit-of-integration So I guess answer is C. 2 votes 2 votes raja11sep commented Nov 14, 2020 reply Follow Share F′(t)=f(t^2)∗2t -f(t)*1 Now, put t=1 ⇒ F′(1) = f(1)∗2 – f(1) ⇒F′(1) = 1∗2 -1 So, F′(1) = 2-1 = 1 (Option C). 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes simply apply Leibnitz and u will get and as 1 Amartya answered May 24, 2020 Amartya comment Share Follow See all 0 reply Please log in or register to add a comment.