Explanation Given: The definite integral ∫ 0 3 4 x 2 e x d x . Formula used: Write the formula for integral of f ( x ) = x n provided n ≠ − 1 . ∫ x n d x = x n + 1 n + 1 + C Write the formula for integral of f ( x ) = e x . ∫ e x d x = e x + C In the above formulae, C is the integration constant. The use of integration constant C is done only for indefinite integrals. Write the formula for derivative of f ( x ) = x n . d d x ( x n ) = n x n − 1 Write the formula for derivative of f ( x ) = e x . d d x ( e x ) = e x The integration by parts for functions u and v is given by the formula: ∫ u d v = u v − ∫ v d u The definite integral of a function f ′ ( x ) from x = a to x = b is calculated by the formula: ∫ a b f ′ ( x ) d x = | f ( x ) | a b = f ( b ) − f ( a ) Calculation: Consider the given definite integral: I = ∫ 0 3 4 x 2 e x d x Use the integration by parts formula to solve for I where u is 4 x 2 and dv is e x d x . Therefore, d u = 8 x d x and v = e x . Write the integration by parts formula. ∫ u d v = u v − ∫ v d u Substitute 4 x 2 for u , e x d x for dv, 8 x d x for du and e x for v . ∫ 0 3 4 x 2 e x d x = | 4 x 2 e x | 0 3 − ∫ 0 3 e x ( 8 x d x ) …… (1) Here, use the integration by parts further to integrate ∫ 0 3 e x ( 8 x d x ) . Write the integration by parts formula. ∫ u d v = u v − ∫ v d u Substitute 8 x for u , e x d x for dv, 8 d x for du and e x for v

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 13, Problem 55RE

To determine

To calculate: The value of the definite integral given below:

∫034x2exdx

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13, Problem 53RE

Chapter 13, Problem 56RE

Students have asked these similar questions

2) Drive the frequency responses of the following rotor system with Non-Symmetric Stator. The system contains both external and internal damping. Show that the system loses the reciprocity property.

1) Show that the force response of a MDOF system with general damping can be written as: X liax) -Σ = ral iw-s, + {0} iw-s,

3) Prove that in extracting real mode ø, from a complex measured mode o, by maximizing the function: maz | ቀÇቃ | ||.|| ||.||2 is equivalent to the solution obtained from the followings: max Real(e)||2

Chapter 13 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.