Riemann Sum & Definite Integral

What does this picture represent?

• left Riemann sum

• right Riemann sum

• midpoint Riemann sum

• trapezoidal sum

What does this picture represent?

• left Riemann sum

• right Riemann sum

• midpoint Riemann sum

• trapezoidal sum

What does picture represent?

• left Riemann sum

• right Riemann sum

• midpoint Riemann sum

• trapezoidal sum

What does "C" represent in an antiderivative?

• a variable

• a constant

• neither of these

What is the approximate area under the curve, using 4 intervals with heights using left values?

• 20

• 14

• 10

• 8

Which of the following definite integrals represent the area of the shaded region? (Scaled by ones)

• $\int_0^3\ \left(x^2+3\right)\ dx$

• $\int_1^3\ \left(x^2+3\right)\ dx$

• $\int_3^1\ \left(x^2+3\right)\ dx$

• $\int_1^3\left(x^{2\ }+3\right)\ dy$

A Riemann sum uses rectangles to ...

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.

What is the approximate area under the parabola using 4 intervals with heights using right values?

• 6

• 10

• 11

• 20

What statement best describes the Riemann sum?

• 4 intervals, with heights using middle values

• 4 intervals, with heights using left values

• 5 intervals, with heights using middle values

• 5 intervals, with heights using right values

Underestimate or overestimate?

• Overestimate
• Underestimate