(a) The volume (growth) of the tumor can be found by integrating the function g (t) with respect to time t. Explain in your own words why this is so. (b) Use the symbols t1 and t2 as the lower and upper bounds of the integral respectively. If t1 is initialized as t1 = 0, calculate what will the value of t2 be? (c) Using your answer in part (b), write down the definite integral that will be used to calculate the volume (growth) of the tumor. (d) Solve the definite integral with an appropriate substitution. (e) State in English what the value of your answer in part (e) describes.
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 this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
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.
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(a) The volume (growth) of the tumor can be found by integrating the function g (t) with respect to
time t. Explain in your own words why this is so.
-
(b) Use the symbols t1 and t2 as the lower and upper bounds of the
integral respectively. If t1 isinitialized as t1 = 0, calculate what will the value of t2 be?
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(c) Using your answer in part (b), write down the definite integral that will be used to calculate the
volume (growth) of the tumor.
-
(d) Solve the definite integral with an appropriate substitution.
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(e) State in English what the value of your answer in part (e) describes.
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