   Chapter 13.2, Problem 36E

Chapter
Section
Textbook Problem

# Evaluate the integral.36. ∫ 1 4 ( 2 t 3 / 2   i  +  ( t  + 1 )   t  k ) d t

To determine

To Evaluate: The integral 14(2t32i+(t+1)tk)dt.

Explanation

Formula used:

Consider the following integral formulae to compute the expression.

tndt=tn+1n+1[f(t)+g(t)]dt=f(t)dt+g(t)dt

To find the integral of the vector function, integrate each component of the vector function.

Integrate each component of the vector function (2t32i+(t+1)tk) in the finite interval of 1 to 4 as follows.

14(2t32i+(t+1)tk)dt=[14(2t32)dt]i+[14[(t+1)t]dt]k=[14(2t32)dt]i+[14[(t+1)t12]dt]k=[14(2t32)dt]i+[14(t32+t12)dt]k

Compute the expression 14(2t32i+(t+1)tk)dt=[14(2t32)dt]i+[14(t32+t12)dt]k by using the formulae as follows.

14(2t32i+(t+1)tk)dt=[14(2t32)dt]i+{[14(t32)dt]dt+[14(t12)dt]}k<

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