# Thread: Graphing and integration problemo

1. ## Graphing and integration problemo

1. graph y=|f(|x|)|

2. If: $2/(x^3+x^2+x+1) = 1/(x+1)-x/(x^2+1)+1/(x^2+1)$

Hence evaluate the definite integral between 0.5 and 2 of $2/(x^3+x^2+x+1) dx$ (to the x-axis) using the above result

2. Originally Posted by Bartimaeus
1. graph y=|f(|x|)|

2. If: $2/(x^3+x^2+x+1) = 1/(x+1)-x/(x^2+1)+1/(x^2+1)$

Hence evaluate the definite integral between 0.5 and 2 of $2/(x^3+x^2+x+1) dx$ (to the x-axis) using the above result
are questions 1 and 2 talking about the same function. as far as question 2 is concerned, just use the partial fractions you were given.

$\int_{0.5}^2 \frac 2{x^3 + x^2 + x + 1}~dx = \int_{0.5}^2 \bigg( \frac 1{x + 1} - \frac x{x^2 + 1} + \frac 1{x^2 + 1} \bigg)~dx$

simple substitutions work for the first two integrals, you may even be able to do them in your head. the last integral is just the arctangent. then evaluate between the points according to the Fundamental Theorem of Calculus

3. One can prove that the original integral equals $\int_{0,5}^{2}{\frac{2x}{x^{3}+x^{2}+x+1}\,dx}$ too. Now, how about makin' $\int_{0,5}^{2}{\frac{2}{x^{3}+x^{2}+x+1}\,dx}+\int _{0,5}^{2}{\frac{2x}{x^{3}+x^{2}+x+1}\,dx}?$