integrate followingint -2 24x 4- x2

Question

Integrate following.

∫ _-2  ²4x ⁴- x²  + 1dx

Solution

In this case the integrand is even & the interval is accurate so,

∫ _-2  ²4x ⁴- x²  + 1dx = 2∫ _o  ²4x ⁴- x²  + 1dx

                                = 2 ( (4/5) x⁵ - (1/3) x³ + x |²₀

                                = 748 /15

Therefore, by using the fact cut the evaluation in half (essentially since one of the new limits was zero).