Use the value of the first integral I to evaluate the two given integrals. IequalsIntegral from 0 to 1 (x cubed minus 5 x )dxequalsnegative nine fourths a. Integral from 0 to 1 (10 x minus 2 x cubed )dx b. Integral from 1 to 0 (5 x minus x cubed )dx

a) (9/2)

b) (9/4)

Step-by-step explanation:

I = ∫¹₀ (x³ - 5x) dx = -(9/4)

a) ∫¹₀ (10x - 2x³) dx = -2 ∫¹₀ (x³ - 5x) dx

∫¹₀ (x³ - 5x) dx = -(9/4) from the given value for I

-2 ∫¹₀ (x³ - 5x) dx = -2 × (-9/4) = (9/2)

b) ∫¹₀ (5x - x³) dx = -1 ∫¹₀ (x³ - 5x) dx

∫¹₀ (x³ - 5x) dx = -(9/4) from the given value for I

-1 ∫¹₀ (x³ - 5x) dx = -1 × (-9/4) = (9/4)

Hope this Helps!!!

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!