(8) (6 marks) An object moves along a line with velocity function given by v(t) = t2 4t + 3. (a) Find the displacement of the particle during 0 S t S 6. (b) Find the distance traveled by particle during 0 g t S 6. (9) (2 marks) Find the interval where the following function g(x) = / et dt is concave up. (10) (3 marks) Find the limit lim Ji th In(t) dt fax sin(t - 1)dt(11) (9 marks) In questions Ila110, rst nd the appropriate substitution, change the integral, and evaluate 2it. (a) 611:2 +4w1 daz- 2$3+2m2$+3 0 Appropriate substitution in : o Integral after the substitution is performed: 0 Evaluate the integral. e2 1 (b) j x(ln(a:))2 d\"; 0 Appropriate substitution u = o Integral after the substitution is performed: 0 Evaluate the integral. 1 (c) f x5\\/ 51:2 + 4 dx 0 0 Appropriate substitution u = o Integral after the substitution is performed: 0 Evaluate the integral