4 votes 4 votes Let $\frac{d}{dx} [f(x)] = \frac{e^{sinx}}{x} , x > 0 .$ If $\int_{1}^{4}(\frac{2e^{sinx^{2}}}{x}) dx = f(k) - f(1)$ where limits of integration is from $1$ to $4$ , then $k =?$ Calculus engineering-mathematics calculus virtual-gate-test-series + – Habibkhan asked Oct 4, 2016 recategorized Apr 2, 2019 by Lakshman Bhaiya Habibkhan 554 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Let x2 = t, Limit value x = [ 1 , 4 ] => t = [ 1 , 16 ] And 2x dx = dt => 2dx / x = dt / x2 = dt / t. ∫ (2 esinx^2 / x) dx = ∫ (esin t ) / t dt = ∫ F ' ( t) dt // d/dx [f(x)] = esinx / x , x > 0 = [F(t) ]116 = F(16 ) - F(1) Ans - k= 16. vijaycs answered Oct 4, 2016 vijaycs comment Share Follow See all 0 reply Please log in or register to add a comment.