Consider the following theorem. Theorem If f is integrable on [a, b], then b a f(x) dx = lim n→∞ n i = 1 f(xi)Δx where Δx = b − a n and xi = a + iΔx. Use the given theorem to evaluate the definite integral. 7 (x2 − 4x + 7) dx 1

Consider the following theorem. Theorem If f is integrable on [a, b], then b a f(x) dx = lim n→∞ n i = 1 f(xi)Δx where Δx = b − a n and xi = a + iΔx. Use the given theorem to evaluate the definite integral. 7 (x2 − 4x + 7) dx 1

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.4: Related Rates

Problem 9E: Assume xand yare functions of t.Evaluate dy/dtfor each of the following. cos(xy)+2x+y2=2; dxdt=2,...

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Question

Consider the following theorem.

Theorem

If f is integrable on

[a, b],

then

f(x) dx = lim n→∞

n

i = 1

f(x_i)Δx

where

Δx =

b − a

and

x_i = a + iΔx.

Use the given theorem to evaluate the definite integral.

7	(x² − 4x + 7) dx

1

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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