hello i have an assignment that i have to submit this Thursday and i really need help. please answer my questions. i have attached the questions sheet in the pdf.

 

 

Due 7 July, 2016
MATH 1004, Section A
Total marks: 80
ASSIGNMENT 2
Solve each of the following integrals by substitution. Some might require pre-conditioning:
Can you apply a trig substitution? Can you break up the integral into 2 fractions because you’ve
got 2 terms over a common denominator? Each question is worth 5 marks (1 for the correct
choice of u, 1 for correctly deriving the needed du expression, 1 for subbing u and du correctly,
1 for using the right antiderivative formula, 1 for your answer).
1.
Z (3x + 1)33 dx Z 4(3 − x)20 dx 2. 3.
Z 2
dx
(2 + x)3 Z 1
dx
(1 − x)2 4. 5.
Z 1+x
dx
1 + x2 6.
Z 2x
√
dx
1 − x2 Z 1 + 2x
√
dx
1 − x2 Z x
√
dx
1 − x4 7. 8. 9.
Z cos x
dx
1 + sin2 x Z cos3 x
dx
1 − sin2 x 10. 11.
sec2 x
√
dx
3
tan x Z 12.
sec x tan x
dx
(1 + tan2 x)3 Z 13.
sec2 x
dx
1 + tan x Z 14.
1
dx
x(ln x)3 Z 15.
Z 1
dx
x(ln(x3 ))3 16.
− tan x
dx
ln(cos x) Z 17.
Z 2x
dx
ln(2x ) 18.
Z 5 x4 ex dx 19.
Z cos x esin x dx 20.
Z csc2 x
dx
ecot x

Attachments:

• 1492837987-ass2.pdf