Math

h.w22.docx

 Interpret the definite integrals as sums and differences of areas and then use simple geometric formulas to evaluate the integrals. In each case sketch the graph of the function. Keep in mind that the area bounded below the X-axis and above the graph of = f(x) contributes as a negative number. (a) ntegral from (-1)^(3) 2 dx . (b) ntegral from (2)^(10) (-1) dx . (c) ntegral from (-1)^(3) (x-1) dx . (d) ntegral from (a)^(b) 2007 dx . (e) ntegral from (-2)^(3) |x-1| dx . (f) ntegral from (0)^(1) root (1-x^2) dx .

 Set up but do not evaluate ntegral from (0)^(1) x^4 dx as the limit of a Riemann Sum. You can choose _i^* as right endpoints of the interaval x_i,x_(i+1)] .

 Set up but do not evaluate ntegral from (2)^(6) e^x sin x dx as the limit of a Riemann Sum. You can choose _i^* as right endpoints of the interaval x_i,x_(i+1)] .

 Set up and then use limits and the formula: um_(i = 1)^(n) i^2 = 1/6 n(n+1) (2 n+1) to find the exact value of ntegral from (0)^(2) 3 x^2 dx . When discussing this problem on the forum please use the formula generator to clearly express math. Submit this problem after you have understood all steps - copying bits from the homework discussion without your own input does not help you learn.