Question

9. (5 points each) Evaluate each of the following. Show all of your work and give exact answers. If the answer is a number, do not round. de = ez dr = () (4 + 2) di

Answer 1

X a) Here given integral is dx. Now substitute u = x² +5 then du = 2.xdx xdx = -du. du. 5 2 Then after substitute u = x² +5 we get, dx = Vx? + 5 du. 2vu Now I zato 1 u du = = 2vu 2 s uždu = * 2už + C(constant) = Vu+C(constant) + C(constant) 1 +1 2 2 X Now by putting the value of u = x² +5 we get, s dx = Vx? +5 +C(constant) -5 e@ еx3 d 1 b) Now we know that I e* dx = for a +0. Then Le**dx = €4-2] = { [e1% -2-10] J*= c) From Leibnitz rule on derivative we get, som f()dr} = (b(x) = 6(x)= f(a(z)) d'(x) where e15 210 db b'(x) = dx da and d'(x) = dx Now then a 1" (+2)dt = (x2 + 2) {<=>3=(1+2) {1} = (x* + 2).27 – 30 – 2x + 4x