Calculate the area of the yellow and red curves using definite integral.

Q: where y=f(x), 8y^2 = x^2-x^4 , of the curve segment X-axis write the surface area of ​​the rotating…

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Q: Use a calculator to find the area under the curve given by y=9x^2+1 between x=0 and x=2 Area:

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Q: S[y] given by y = cosh æ + B sinhx, 0 0,

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Q: How were the boundaries on the integral calculated?

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Q: Find the area between two curves: y=2x-x^2+3 y=x^2-4x+3 Show steps of calculation.

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Q: Given a rate of 175 pesos per hour, how many hours should you work to earn 35,962.50 pesos

A: If ∆x is the amount earned in time ∆t, then the equation for the rate of the amount earned per unit…

Q: Find the area between the curve y= 2x +10 and line y4x + 16 64 64/5 64/3 O 64/7

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Q: Calculate ∫∫(x^2 + y^2)^3 dA. Where D is the region in the first quadrant                  D…

A: Concept Used:- In polar coordinates x=r cosθy=r sinθ ⇒x2+y2=r2 Consider the region D bounded by y=x,…

Q: 3/ find the area for the region in the first quadrant bounded by the curve (y = 4x - x²) and line (y…

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Q: what about line and surface integrals??

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Q: The curve below shows the rate t, in hours, that a tank is leaking. To find the total amount of…

A: Create smal rectangles of width

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.