Question

(a)

i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0)

Make the substitution u=2x^2−4x+2, and write the integrand as a function of u,

∫(4x−4)(2x^2−4x+2)^4 dx =∫

and hence solve the integral as a function of u, and then find the exact value of the definite integral.

ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u.

∫ e^(3x)dx/36+e^(6x)=∫

Hence solve the integral as a function of u, including a constant of integration c, and then write the integral as a function of the original variable (x and c).

Answer 1

.. Guven meghal J. 4x 4) (2x42 dx Noro bstituti ehen ofhen and when , then

lve have Ls O u duy u du ts Hence 4 Lue have U-2. 5 Lu (2)5 (a)5] 5 32 o 3 2 Hence 3 2

I .: Give n integrat 3x 36 + e 3x we hav 6Y 36 t 3 6 dlx 36 8 6 36ter 3 twe have 3x ーしー( 96 2du + 42 36 t.eex-dx. 18 +Lt ck 36 + e(x Now e integiathon 3 2x ウ 36+er + C ie