Definite Integrals

Definite Integrals Warmup


The graph of the function y=f(x)y = f(x) is shown above. What is the value of 06f(x)dx?\int_0^6 f(x) dx?

Steve knows that if he uses right-hand endpoints with 2 subintervals to find a Riemann sum approximation of 08xdx,\int_0^8 x dx, his approximation will be the sum of the areas of the 2 rectangles shown. Assuming all his work is correct, what will his approximation be?

Morgan and Pat use right-hand endpoints to find Riemann sum approximations of 08xdx.\int_0^8 x dx.

If Morgan uses 2 subintervals, and Pat uses 4 subintervals, whose approximation is closer to the true value of the integral?

Ferb knows that 08xdx=32,\int_0^8 x dx = 32, and is interested in how close a right-hand Reimann sum approximation to the integral can be.

Based on his work so far, if Ferb uses 32 subintervals, what will his approximation be?

Number of subintervalsApproximationError

A=12xdx,B=12x2dx A = \int_{1}^{2} x dx, \,\,\,\, B = \int_{1}^{2} x^2 dx

Which of the following is true of AA and B?B?


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