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u² = 2 + xx = u² - 2dx/du = 2u
ʃ x(2 + x))^1/2 dx= ʃ xu dx= ʃ u(u² - 2) dx= ʃ 2u² (u² - 2) du= ʃ 2u⁴ - 4u² du= [...

The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. x...

This is an example of a question where we would have to use the product rule for differentiation, because we have two functions multiplied together ( x and ln(2x) ).If we have: y = uv, where u and v are f...

Y=(x+5)(x+3) ............(1)The above expression on the right is a product of two expressions,Hence, product rule differentiation method will be employed as stated below:Y(u,v)=U(x).V(x) .........(2)dy/dx...

We can use integration by parts to solve this question. If we look at the formula for Integration by parts: ∫u(dv/dx)dx = uv - ∫ v (du/dx) dx, we see that u must be multi...