# Thread: did i do these correctly?

1. ## did i do these correctly?

1) Find the area enclosed by the curves $\displaystyle y=x^2$ and y=x
My answer: $\displaystyle \frac{1}{6}$

2) Find the area bounded by the curves: $\displaystyle x=-y^2$ and $\displaystyle x=-y-2$
My answer: $\displaystyle \frac{-9}{2}$

3) Evaluate: $\displaystyle \int \frac{2x}{(x^2+1)^3} dx$

My answer: $\displaystyle \frac{-1}{2}(x^2+1)^{-2}+c$

4) Find the equation of the tangent line to y=sin(3x) where $\displaystyle x=\pi$
My answer: $\displaystyle y=-3(x-\pi)$

If any of my answers are incorrect then please let me know which one(s).

2. Originally Posted by yoman360
1) Find the area enclosed by the curves $\displaystyle y=x^2$ and y=x
My answer: $\displaystyle \frac{1}{6}$

2) Find the area bounded by the curves: $\displaystyle x=-y^2$ and $\displaystyle x=-y-2$
My answer: $\displaystyle \frac{-9}{2}$

3) Evaluate: $\displaystyle \int \frac{2x}{(x^2+1)^3} dx$

My answer: $\displaystyle \frac{-1}{2}(x^2+1)^{-2}+c$

4) Find the equation of the tangent line to y=sin(3x) where $\displaystyle x=\pi$
My answer: $\displaystyle y=-3(x-\pi)$

If any of my answers are incorrect then please let me know which one(s).
1, 3, and 4 look okay. Not sure about 2. If they are asking for area, it should be a positive amount.

3. #2. The answer should be 9/2. You should integrate -y^2 + y + 2 and your bounds for integration are -1 and 2. Doing so will lead to a positive value 9/2