LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals

The integral of (1 + 1/t)^3 (1/t^2)
u= 1+ 1/t du= -1/t^2
Multiply the integral by a negative since there is not any in the problem
- integral u^3
- 1/4 u^4
-1/4 (1+ 1/t)^4 +c

Find the volume of the solid obtained by rotating about the x-axis the region under the curve from -2 to 1: y=sqroot(-2x^2-10x+48)

the sq root dissapearas and you then have to integrate the equation.
after you intergrate you plug in : top- bottom times pi.

-2/3(x)^3-5x^2+48x

top-bottom: -2/3(1)^3-5(1)^2+48(1)-(-2/3(-2)^3-5(-2)^2+48(-2))

=491/3.
=491(pi)/3.


for some reason i just can't do the tangent line problems on the ap test, idk where i'm going wrong.