1. graph y=|f(|x|)|
2. If: $\displaystyle 2/(x^3+x^2+x+1) = 1/(x+1)-x/(x^2+1)+1/(x^2+1)$
Hence evaluate the definite integral between 0.5 and 2 of $\displaystyle 2/(x^3+x^2+x+1) dx$ (to the x-axis) using the above result
1. graph y=|f(|x|)|
2. If: $\displaystyle 2/(x^3+x^2+x+1) = 1/(x+1)-x/(x^2+1)+1/(x^2+1)$
Hence evaluate the definite integral between 0.5 and 2 of $\displaystyle 2/(x^3+x^2+x+1) dx$ (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.
$\displaystyle \int_{0.5}^2 \frac 2{x^3 + x^2 + x + 1}~dx = \int_{0.5}^2 \bigg( \frac 1{x + 1} - \frac x{x^2 + 1} + \frac 1{x^2 + 1} \bigg)~dx$
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