Raghad A.
asked • 04/20/23what is the area of y=5x/1+x^2, y=5x^2/1+x^3 in terms of ln please
what is the area of y=5x/1+x^2, y=5x^2/1+x^3
in terms of ln please
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1 Expert Answer
Dayv O. answered • 04/20/23
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Caring Super Enthusiastic Knowledgeable Calculus Tutor
∫[[5x/(1+x2)]-[5x2/(1+x3)]]dx ,,,integral of top curve - bottom curve (for x=0 to 1)
=(5/2)ln(1+x2)-(5/3)ln(1+x3)+C
evaluated x=0 to x=1
area = (5/6)ln2
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Doug C.
I am guessing the problem statement has omitted that you are finding the area between the two curves in the 1st quadrant. Also when you use the "/" to define a fraction when there is more than one term in numerator and/or denominator, use grouping symbols, e.g. 5x/(1+x^2). Visit the following graph, take some notes and respond here if you need additional clarification: desmos.com/calculator/z7n1fpyjay04/20/23