# Calculating Areas using Integrals - Page 4

Questions

- How do you find the area between two curves using integrals?
- How do you find the center of mass if the density at any point is inversely proportional to its distance from the origin of a lamina that occupies the region inside the circle #x^2 + y^2 = 10y# but outside the circle #x^2+y^2=25#?
- How do you find the area of the region bounded by the curves #y=sin(x)#, #y=e^x#, #x=0#, and #x=pi/2# ?
- How do you sketch the region enclosed by #y=1+sqrtx, Y=(3+x)/3# and find the area?
- How do you find the area between #x=4-y^2# and #x=y-2#?
- How do you find the area of an ellipse using integrals?
- If #y'(x)+y(x)g'(x)=g(x)g'(x)" ; y(0)=0 ; g(0)=g(2)=0 " where " x in RR# then #y(2)=?#
- How do you find the area between #y=x^2# and #y=8x#?
- Find the area of the region bounded by the curves?
- How do you sketch the region enclosed by #y=x^2-2x, y=x+4# and find the area?
- If 2 curves #y=kx^n# and #y=lnx# have the same gradient exactly at x=a, find the relationship between a, k and n? Also, if these 2 curves also intersect at the point x=a, express k in terms of n?
- How to answer these using intergration ?
- How do you find the area bounded by the x axis, y axis and x+y=4?
- How do you find the area between #f(x)=x^2-4x+3# and #g(x)=-x^2+2x+3#?
- How do you find the area of the region bounded by the curves #y=tan(x)# and #y=2sin(x)# on the interval #-pi/3<=x<=pi/3# ?
- How do you find the area between #f(y)=y^2, g(y)=y+2#?
- How do you find the area bounded by #y=x#, #y=1/x^2# the x axis, and x=3?
- How do you find the area bounded by #x=8+2y-y^2#, the y axis, y=-1, and y=3?
- Please explain geometric and harmonic progressions?
- Find # int int \ e^(x^2+y^2) \ dA # over the region bounded by #y = sqrt(9-x^2)#?