Use a definite integral to find the area under the graph of y = 3x2 from x = 0 to x = 1.

Q: Estimate the area under the graph of f(x) = x? + 2x from x = 1 to x = 7 using 3 approximating…

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Q: Find the area below the curve f(x) = √√4-x4 2x from x = 0 to x = √√2

A: The objective of this question is to find the area under the curve defined by the function f(x) =…

Q: What number a>0 makes it that the area under the function f(x)=sin(2x) between x=0 and x=a is 1

A: The area under f(x) and between x=0 and x=a is given by: Given that this equals 1.  We have to…

Q: Calculate the integral of y = 11 cos (8x) from 0 to Answer = Number Leave your answer in exact form…

A: on solving this we get the

Q: What is the area under the curve of the following positive function y = 10x4 + 3x² between x = -1…

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Q: Find the area under the graph of y = 2x² - 2x + 4 on the interval [-2,0].

A: y=2x2−2x+4 on the interval [−2,0]

Q: The Area between k*x3 and k*sin (x) is 2. What is the value of k?

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Q: Find the area under the curve between x-2 and x=-1 for the curve f(x)=(7 – x²)d

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Q: Estimate the area under the graph of f(x) = 1 + x 2 from x = −1 to x = 2 using three rectangles and…

A: To find the area under the graph of f(x)=1+x2 from x = −1 to x = 2 using three rectangles and right…

Q: Estimate the area under the graph of f(x) = 2x + 16x + 35 over the interval (0, 4] using ten…

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Q: Estimate the area under the graph of f(x) = x² – 2x + 5 over the interval (0, 7 using ten…

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Q: Find the area under the graph of f(x) = x² + 10 between x = 0 and x = Area = 6.

A: Givenf(x) = x² + 10x = 0 & x = 6

Q: Estimate the area under the graph of f(x)= rectangles and right endpoints. R₁ 1 over the interval…

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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.