Hi , every one. I need help to solve these calculus
problems, the question is:
1-Find the area under the given curves:
a) y = 6x^3 + 6x^2 - 6x between x = 1 and x = 3
b) f(x) = -3e^-3x -3X between x = 0 and x = 2
and other question:
Solve the following differential equations:
a) dy/dx=3x^2 b) dy/dx=3e^3x
c) dy/dx=3xy c) dy/dx=1/(y+1)^2 x e^3x
With my thanks to any try.....
Adam12

Question

Hi , every one. I need help to solve these calculus
problems, the question is:
1-Find the area under the given curves:
a)  y = 6x^3 + 6x^2 - 6x between x = 1 and x = 3
b) f(x) = -3e^-3x -3X  between x = 0 and x = 2
and other question:
Solve the following differential equations:
a) dy/dx=3x^2       b) dy/dx=3e^3x
c) dy/dx=3xy         c) dy/dx=1/(y+1)^2  x   e^3x
With my thanks to any try.....
Adam12

anonymous · Answer

$$\int\limits_{0}^{2}-3e ^{-3x}-3x = [e ^{-3x}-(3/2)x ^{2}  ] _{0}^{2}$$

anonymous · Answer

then plug in the values and solve

anonymous · Answer

$$A = \int\limits_{1}^{3} y dx$$ $$A = \int\limits_{1}^{3} [6x ^{3} + 6x ^{2} - 6x] dx$$
$$\left[ 1.5 x ^{4}+2x ^{3}-3x ^{2}\right]_{1}^{3}$$

anonymous · Answer

here's the clue for differential $$[dy/dx= ax ^{n} ] = nax^{n-1} , [dy/dx=ae^{nx}] = nae^{nx}$$

anonymous · Answer

Thank you very much, I rally appreciate your effort
answering these problems.

anonymous · Answer

you're welcome.. if u have any problems again message me, i'm ready to help ..