1.

Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) /2 5 In(x) dx, n=10 1 1+x (a) the trapezoidal rule ) (b) the midpoint rule T (c) Simpson's rule L) Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 1./.2 / 4sin(e\"2)dt, n=8 o (a) the trapezoidal rule | (b) the midpoint rule H (c) Simpson's rule H (a) Find the approximations 710, M10, and S10 for / 19 sin(x) dx. (Round your answers to six decimal places. ) T10 = M10 = S10 Find the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. ) ET = EM (b) Compare the actual errors in part (a) with the error estimates found by using the smallest possible values for K in the theorem about error bounds for trapezoidal and midpoint rules theorem about error bound for Simpson's rule. (Round your answers to six decimal places.) |Esl S (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T,, M,,, and S,, to the integral in part (a) are accurate to within 0.00001? For T , n= For M, n = For S, n =The table below gives the power consumption P in megawatts in a county from midnight to 6:00 a.m. on a day in December. Use Simpson's rule to estimate the energy used during that tir (Use the fact that power is the derivative of energy. Round your answer to one decimal place.) 0:00 | 1,816 | 3:30 | 1,617 0:30 | 1,733 | 4:00 | 1,623 1:00 | 1,684 | 4:30 | 1,664 1:30 | 1,646 | 5:00 | 1,747 2:00 | 1,637 | 5:30 | 1,884 2:30 | 1,605 | 6:00 | 2,054 3:00 | 1,602 megawatt-hours Consider the following table of function values. (a) Use the Midpoint Rule with n 3.2 / f(x) dx Jo (b) x f(x) x f(x) 0.0 | 6.9 | 2.0 | 6.5 0.4 | 8.1 24 | 6.5 08| 73 | 28| 6.6 1.2 | 6.8 | 3.2 | 6.3 1.6 1.7 [N [ ] 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.) A Suppose it is known that 4 x+1 /1 43mr1.1 O convergent O divergent Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) /77de 1 X Need Help? Read It Determine whether the integral is convergent or divergent. =2 e Xx(In x)3 O convergent O divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 33 ) / 21(.r1)71"'5(l.r 0 O convergent O divergent Determine whether the integral is convergent or divergent. 2222 In z dz O convergent O divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)