List of top Mathematics Questions on Calculus asked in NATA

f \(\int_0 ^a3x^2dx=8\) then find the value of a

If \( x = t \) and \( y = \frac{1}{t} \), then \(\frac{dy}{dx}\) is equal to:

Evaluate the integral. \(\displaystyle\int^{3}_{2}x^4dx\)

The differential equation of all non vertical lines in a plane is:

The value of \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (x^2 \sin x + x^3) \, dx\) is:

Solution of the differential equation\( \frac{dy}{dx}=y^2\) with the condition y(1)=1 is