Question

What is the integral of (3t - 1)3 dt?

Answer 1

Step-by-step explanation:

The answer is t³/3 + 3t⁴/4 + C

Answer 2

Step 1

We first find the slope of the tangent for which we need derivative of f(x).

f'(x)=d/dx (3x^3+3x^2+x+1)

=3d/dx (x^3)+2d/dx (x^2)+d/dx (x)+d/dx(1)

=3*3x^2+2*2x+1+0

=9x^2+4x+1

Step 2

Now, slope is the value of f’(x) at the given point x = 1.

slope = f'(x)|x = 1 = f'(1) = 9+4+1 = 14

Step 3

Now, to find any one point on the tangent line, we consider the fact that tangent line is drawn at x=1.

f (x)|x = 1= f (1) =:3+2+1+1 = 7