Summation

16 practice questionsIntegral CalculusStep-by-step solutions

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Using summation properties, evaluate $\sum_{i=1}^{7} 5i^2$

A.130

B.96

C.140

D.28

E.None

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Find the mean value of $y=\sin x$ between $x=0$ and $x=\pi$ .

\dfrac{2}{\pi}

\dfrac{1}{\pi}

\dfrac{2}{\pi^2}

\dfrac{\pi}{2}

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In converting a Riemann sum $\sum_{i} f(x_i)\Delta x$ into a definite integral, what happens to the discrete index $i$ and the discrete sample points $x_i$ in the limit?

A.The discrete sum becomes a continuous integral, the index

i

disappears, and the discrete points

x_i

are replaced by the continuous variable

x

ranging over

[a,b]

B.The index

i

becomes the new variable of integration in place of

x

C.The sample points

x_i

must all coincide at a single point in the limit

D.Nothing changes; the Riemann sum and the integral are different objects that happen to have the same numerical value only by coincidence

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Summation

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