Explanation Given Information: The provided integral is ∫ 0 2 x 2 x 2 + 1 d x . Formula used: According to the Fundamental Theorem of Calculus if f is a continuous function defined on the interval [ a , b ] and F is any anti-derivative of f defined on the interval [ a , b ] then, ∫ a b f ( x ) d x = F ( b ) − F ( a ) The constant multiple rule, ∫ k ⋅ f ( x ) d x = k ∫ f ( x ) d x where k is a constant The power rule for the indefinite integral, ∫ x n d x = x n + 1 n + 1 + C , valid for the condition n ≠ − 1 , where C is the constant of integration. Calculation: Consider the provided integral ∫ 0 2 x 2 x 2 + 1 d x , To calculate the integral ∫ 0 2 x 2 x 2 + 1 d x compute the anti-derivative of the integral ∫ 0 2 x 2 x 2 + 1 d x . Assume a function u in terms of x from x 2 x 2 + 1 , u = 2 x 2 + 1 Now, differentiate the function u = 2 x 2 + 1 both sides with respect to x , where, u is the any function of x d u d x = 4 x x d x = d u 4 Solve for d x , x d x = d u 4 Now, calculate the new value of limits by substituting the value of x in the equation u = 2 x 2 + 1 , When x = 0 , then u = 2 ( 0 ) 2 + 1 = 0 + 1 = 1 When x = 2 , then u = 2 ( 2 ) 2 + 1 = 2 ( 2 ) + 1 = 4 + 1 = 5 Now substitute u

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 13.4, Problem 26E

To determine

To calculate: The solution of the integral ∫02x2x2+1 dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.4, Problem 25E

Chapter 13.4, Problem 27E

Students have asked these similar questions

The average amount A (in pounds per person) of fish and shellfish consumed in the UnitedStates during the period 1992–2001 can be modeled by A = (3.2x + 260)/(52x + 3800) where x is the number of years since 1992.Rewrite the model so that it has only whole number coefficients. Then simplify the model.

In Exercises 87–88, use the graph of f(x) = |4 – x| to solve each equation or inequality. y flx) = |4 – x| y = 53- y = 1 $ 9 10 87. 14 - x| = 1 88. 14 - x| < 5

Exercises 101–103 will help you prepare for the material covered in the next section. Use the graph of function f to solve each exercise. 5- 4- 3- 2- 1- -5-4 1 2 3 45 y = flx) 101. For what values of x is the function undefined? 102. Write the equation of the vertical asymptote, or the vertical line that the graph of f approaches but does not touch. 103. Write the equation of the horizontal asymptote, or the horizontal line that the graph of f approaches but does not touch.

Chapter 13 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

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

The solution of the integral ∫ 0 2 x 2 x 2 + 1 d x .

Solution Summary: The author explains the fundamental theorem of calculus, where f is a continuous function defined on the interval left[a,bright] and F is any anti-derivative of

Videos

To calculate: The solution of the integral ∫02x2x2+1 dx.

Want to see the full answer?

Chapter 13 Solutions