Definite Integrals

Definite Integrals Warmup


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

Steve knows that if he uses right-hand endpoints with 2 subintervals to find a Riemann sum approximation of \[\int_0^8 x dx,\] 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 \[\int_0^8 x dx.\]

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

Ferb knows that \[\int_0^8 x dx = 32,\] 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

\[ A = \int_{1}^{2} x dx, \,\,\,\, B = \int_{1}^{2} x^2 dx \]

Which of the following is true of \(A\) and \(B?\)


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