Answer:
A) -9/2
B) 9/4
C) -9/2, same as A)
Step-by-step explanation:
We are given that [tex]I=\int_0^3 x^3-4x dx=9/4[/tex]. We use the properties of integrals to write the new integrals in terms of I.
A) [tex]\int_0^3 8x-2x^3 dx=\int_0^3 -2(x^3-4x) dx=-2\int_0^3 x^3-4x dx=-2I=-9/2[/tex]. We have used that ∫cf dx=c∫f dx.
B) [tex]\int_3^0 4x - x^3 dx=-\int_0^3 (4x-x^3) dx=\int_0^3-(4x-x^3) dx=\int_0^3 x^3-4x dx=I=9/4[/tex]. Here we used that reversing the limits of integration changes the sign of the integral.
C) It's the same integral in A)
