0 votes 0 votes $$\frac{d}{dx}\int_{1}^{x^4} sect\space dt$$ Calculus calculus integration + – `JEET asked Jan 20, 2019 `JEET 439 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply kd..... commented Jan 20, 2019 reply Follow Share integration of sect is ln|sect + tant| thereafter substitute t2=x^4 and t1=1 Then you got result in terms of x which you have to do differentiation wrt x 0 votes 0 votes newdreamz a1-z0 commented Jan 20, 2019 reply Follow Share it is based on lebnitz's rule: $\frac{\mathrm{d} }{\mathrm{d} x}\int_{v(x))}^{u(x))}f(t)dt$=f(u(x))$\frac{\mathrm{d} }{\mathrm{d} x}$(u(x))-f(v(x))$\frac{\mathrm{d} }{\mathrm{d} x}$(v(x)) =sec($x^{4}$)*4$x^{3}$ 3 votes 3 votes `JEET commented Jan 21, 2019 reply Follow Share @newdreamz a1-z0 How you got sec in the answer. I applied the same formula and got $x^44x^3$ 0 votes 0 votes Please log in or register to add a comment.