SOLUTION: Find the area under the curve:
y = 4x + (1/x2) from x = 1 to x = 4
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Question 369761: Find the area under the curve:
y = 4x + (1/x2) from x = 1 to x = 4
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Assuming the equation is
(Please use "^" to indicate exponents.)
The answer will the the value of the definite integral:
Since integrals of powers of x are simple, I am going to rewrite the second term as the appropriate power of x:
Next we can use a property of integrals that tells us the the integral of a sum is the same as the sum of the integrals:
Next we can factor out the 4 in the first integral using a property of integrals:
Each integral is now a power of x. In general . Using this on both of our integrals we get:
evaluated from x=1 to x=4
This simplifies as follows:
evaluated from x=1 to x=4
evaluated from x=1 to x=4
Evaluating this expression from 1 to 4:
Simplifying:
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