Jawab:

64512

Penjelasan dengan langkah-langkah:

In order to solve this integral, we must first use the substitution u = 4 + x^2.

We have dx = (2x/u)du, so our integral becomes:

∫(x^7)/(u) (2x/u) du from -10 to 10

= 2 ∫(x^6)/(4+x^2) du from -10 to 10

Letting u = 4 + x^2, we get:

∫(x^6)(1/(4+x^2))du from 16 to 44

= ∫16+(44-16)(t^5 / 5) dt from 0 to 1 --| let t = (4+x^2 - 16)/ 28

--| du = 28 dt

--| t = 0 and t = 1 when u = 16 and u = 44 respectively

= (44-16)(1/5 1/6 1 cube + 1/7 1/8 3 cube + .... +1/33 1/34 5 cube)

-- |integral of a GP with ratio of two terms being (1/n) and nth terms being n cube where n ranges from 6 to 34 in steps of 2

= 64512