Explanation Given: The equation of curve is y = ( 3 + x 2 ) e 2 x and x from x = 0 to x = 1 Approach: If f ( x ) is a continuous function of x on the closed interval [ a , b ] Then the area of the region bounded by f ( x ) and x axis is given as: A = ∫ a b f ( x ) d x Then we can evaluate integral as given below Integral by parts- It is a method of integration when two function multiplied together. ∫ ( u v ) d x = u ∫ v d x − ∫ u ' ( ∫ v d x ) d x In this u , v is the function of x and u ' is derivative of x Calculation: Given equation of curve is y = ( 3 + x 2 ) e 2 x and x from x = 0 to x = 1 Then area of curve is A = ∫ 0 1 ( 3 + x 2 ) e 2 x d x In this u = ( 3 + x 2 ) , v = e 2 x ∫ 0 1 ( 3 + x 2 ) e 2 x d x = [ ( 3 + x 2 ) × ∫ e 2 x d x − ∫ d d x ( 3 + x 2 ) ( ∫ ( e 2 x ) d x ) d x ] 0 1 = [ ( 3 + x 2 ) × e 2 x 2 − ∫ 2 x × e 2 x 2 d x ] 0 1 = [ ( 3 + x 2 ) × e 2 x 2 − ∫ x e 2 x d x ] 0 1 = [ ( 3 + x 2 ) × e 2 x 2 − ∫ x e 2 x d x ] 0 1 Simplify further,

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ISBN: 9780321964038

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

Publisher: Pearson Addison Wesley,

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Chapter 8.CR, Problem 39CR

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Area between curve and of x-axis y=(3+x2)e2x in given interval from x=0 to x=1.

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Chapter 8.CR, Problem 38CR

Chapter 8.CR, Problem 40CR

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Area between curve and of x -axis y = ( 3 + x 2 ) e 2 x in given interval from x = 0 to x = 1 .

Solution Summary: The author explains that the area bounded by region is 74(e2-1)approx 11.18.

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To find:

Area between curve and of x-axis y=(3+x2)e2x in given interval from x=0 to x=1.

Want to see the full answer?

Chapter 8 Solutions

Area between curve and of x -axis y = ( 3 + x 2 ) e 2 x in given interval from x = 0 to x = 1 .

Solution Summary: The author explains that the area bounded by region is 74(e2-1)approx 11.18.

Videos

To find: Area between curve and of x-axis y=(3+x2)e2x in given interval from x=0 to x=1.

Want to see the full answer?

Chapter 8 Solutions

To find:

Area between curve and of x-axis y=(3+x2)e2x in given interval from x=0 to x=1.