Evaluating a Definite Integral Using a Geometric Formula In Exercises 27-36, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r > 0). ∫ − 1 1 ( 1 − | x | ) d x
Evaluating a Definite Integral Using a Geometric Formula In Exercises 27-36, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r > 0). ∫ − 1 1 ( 1 − | x | ) d x
Solution Summary: The author explains how to calculate the value of the provided integral using geometric formula and graph it.
Evaluating a Definite Integral Using a Geometric Formula In Exercises 27-36, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r > 0).
∫
−
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1
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d
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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.
Tutorial Exercise
Use the form of the definition of the integral given in the theorem to evaluate the integral.
(1 + 5x) dx
-2
Area Function
a) Find the formula for the area function, A(x), represented by the integral.
b) Use that formula to find both A(t) and A(2t).
c) Graph f(t) = sin (;t) and shade the area for the interval [0, 27].
d) Graph A(x) on the same graph and plot the point (2r, A(2n)).
e) What is the relationship between parts (c) and (d)?
sin
dt
Using the fundamental theorem, find the area under the curve y = 4x3 −2x+5 and above x-axis on the interval [0,2]
Chapter 5 Solutions
Bundle: Calculus: Early Transcendental Functions, 6th + WebAssign Printed Access Card for Larson/Edwards' Calculus, Multi-Term
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