Express the limit below as a definite integral. The n points Xo...

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Express the limit below as a definite integral. The n points Xo <x₁ <x2 <x<x evenly divide the interval [a,b] into n subintervals, each of width b-a W= . Do not evaluate the definite integral. n 1 n-1 lim w + + +...+ where a 3, b 4. 2 2 2 2 noo The definite integral is (Type an expression using x as the variable.) 元 J4si Approximate 4 sin xdx using three equal subintervals. 0 An approximation for the integral using three equal subintervals is (Type an exact answer, using it as needed.) A rain gauge is set up to measure the amount of total rainfall occurring in 1 hr on campus (the readout from the rain gauge is in mm/hr). The total 6 amount of rainfall between t=0 and t = 6 is given by fr(t)dt. Assume the 0 data to the right is collected in a 6-hour window. Use this information to answer parts (a) and (b) below. Time, t Rainfall rate, r(t) in mm/hr 0 2451100 8123456 (a) Use six even subintervals to approximate the total rainfall between t=0 and t=6 as a sum of areas of rectangles and evaluate this sum using the data in the table. The total rainfall using six even subintervals is approximately ☐ mm. Express the limit below as a definite integral. The n points Xo <x₁ <x2 <x<x evenly divide the interval [a,b] into n subintervals, each of width b-a W= . Do not evaluate the definite integral. n 1 n-1 lim w + + +...+ where a 3, b 4. 2 2 2 2 noo The definite integral is (Type an expression using x as the variable.) 元 J4si Approximate 4 sin xdx using three equal subintervals. 0 An approximation for the integral using three equal subintervals is (Type an exact answer, using it as needed.) A rain gauge is set up to measure the amount of total rainfall occurring in 1 hr on campus (the readout from the rain gauge is in mm/hr). The total 6 amount of rainfall between t=0 and t = 6 is given by fr(t)dt. Assume the 0 data to the right is collected in a 6-hour window. Use this information to answer parts (a) and (b) below. Time, t Rainfall rate, r(t) in mm/hr 0 2451100 8123456 (a) Use six even subintervals to approximate the total rainfall between t=0 and t=6 as a sum of areas of rectangles and evaluate this sum using the data in the table. The total rainfall using six even subintervals is approximately ☐ mm.