Calculus 2 Midterm
∫xⁿdx - ✅✅-(xⁿ⁺¹/n+1)+C
∫cosxdx - ✅✅-sinx + c
∫sinxdx - ✅✅--cosx + c
∫1/x dx - ✅✅-ln |x| + C
pythagorean identities - ✅✅--sin²x+cos²x=1
-1+tan²x=sec²x
-cot²x+1=csc²x
double angle identity - ✅✅-sin(2x)=2sin(x)cos(x)
area between curves - ✅✅-∫(yupper-ylower)dx
equation for a circle - ✅✅-x²+y²=r²
disk method - ✅✅-π∫(f(x))²dx
washer method - ✅✅-V = π∫([R(x)]²-[r(x)]²)dx
shell method - ✅✅-2π∫xf(x)dx
arc length - ✅✅-∫√(1+f'(x)²)dx
surface area formula - ✅✅-∫2πf(x)*√(1+f'(x)²)dx
integration by parts formula - ✅✅-∫udv= uv - ∫vdu
d/dx sin⁻¹x - ✅✅-1/√(1-x²)
d/dx ln|x| - ✅✅-1/x
d/dx tan⁻¹x - ✅✅-1/(1+x²)
half-angle/reduction identities - ✅✅-cos²x=1/2(1+cos(2x))
d/dx secx - ✅✅-secx*tanx
d/dx tanx - ✅✅-sec²x
∫xⁿdx - ✅✅-(xⁿ⁺¹/n+1)+C
∫cosxdx - ✅✅-sinx + c
∫sinxdx - ✅✅--cosx + c
∫1/x dx - ✅✅-ln |x| + C
pythagorean identities - ✅✅--sin²x+cos²x=1
-1+tan²x=sec²x
-cot²x+1=csc²x
double angle identity - ✅✅-sin(2x)=2sin(x)cos(x)
area between curves - ✅✅-∫(yupper-ylower)dx
equation for a circle - ✅✅-x²+y²=r²
disk method - ✅✅-π∫(f(x))²dx
washer method - ✅✅-V = π∫([R(x)]²-[r(x)]²)dx
shell method - ✅✅-2π∫xf(x)dx
arc length - ✅✅-∫√(1+f'(x)²)dx
surface area formula - ✅✅-∫2πf(x)*√(1+f'(x)²)dx
integration by parts formula - ✅✅-∫udv= uv - ∫vdu
d/dx sin⁻¹x - ✅✅-1/√(1-x²)
d/dx ln|x| - ✅✅-1/x
d/dx tan⁻¹x - ✅✅-1/(1+x²)
half-angle/reduction identities - ✅✅-cos²x=1/2(1+cos(2x))
d/dx secx - ✅✅-secx*tanx
d/dx tanx - ✅✅-sec²x
