The value of A00 is, 1 1 :// xydxdy A00 0 0 4 The value of Amo is, 1 1 Amo = 2 ху cos mлxdxdy 0 0 1 cOS mл — 1 -ydy m² n? = 2 (-1)" –1 %D m² n2

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A: ∫x34+9x14 dx Now put, x34+9=tDifferentiating with respect to x, we get⇒34x34-1+0=dtdx…

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Q: dx 3x? — 10х + 15

A: Let I be the integration that we need to find.

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Q: (x² – 3)(x² + 2) 3. dx

A: We need to evaluate ∫(x2-3)(x2+2)x3dx = ∫x4-3x2+2x2-6x13dx= ∫x4-x2-6x13dx= ∫x4-13-x2-13-6x-13 dx=…

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A: For integration by trigonometric substitution problems, Depending on the function we need to…

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A: Given integral is By using the results, we get

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A: To find the following indefinite integral.∫x3x-4 dx

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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.