advertisement

Math 105, Assignment 3 Due 2015-02-25, 4:00 pm In the following problems you are expected to justify your answers unless stated otherwise. Answers without any explanation will be given a mark of zero. The assignment needs to be in my hand before I leave the lecture room or you will be given a zero on the assignment! Don’t forget to staple your assignment! You will lose a mark if you do not. 1. Use the definition of integral and the mid point rule to to show that Z b b3 x2 dx = . 3 0 You cannot use fundamental theorem to solve this. 2. Evaluate the following sum. 2i n X ie n lim n→∞ i=1 n2 Hint: Find a suitable function f and limits a, b and write the above in the form Z b f (x)dx a and apply fundamental theorem. 3. Find the derivative of Z ex 2 log(t2 )dt log x 4. Find the regions where f (x) is increasing Z f (x) = 0 x2 1−t dt 1+t 5. Evaluate the following: Z x dx (a) x+1 Z (b) x2 (x + 1)3/2 dx Z (c) 3 √ 9 − x2 dx (Hint: use geometry) −3 2015 Z sin(x2015 ) − x2015 dx (Hint: don’t use FTC) (d) −2015 Z (e) (log x)2 dx 1 Z π2 (f) √ sin( x)dx 0 Z (g) t es cos(t − s)ds 0 2