Determine if the following integrals converge or diverge by using the indicated tests next to them. -x + 2r? + e4r 2.r3 – r³ Arcsecr – e-2r dr (DCT) Vīlnx + a-/2 3/2 + Arcsecr + Inx b) -dr (LCT)

Q: c) f t√t + 4 dt e) S X 25+16x² dx 25+16x² d) f 25 dx x (19wansoy dilquma) dx 25+16x² f) S

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Q: Give a geometric argument that explains why the integrals have equal values.

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Q: Consider the integral dx, (x² + a²)³/2 where a is a positive real number.

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Q: Give a geometric argument that explains why the integrals have equal values.

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Q: 2x 35. x2 + 6x + 13 -бх + 13

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Q: find formulas for the functions represented by the integrals.

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Q: Evaluate the integral of dx/sqrt(x2+4) without using the right triangle method.

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Q: Solve by using u-sub  Find integral  3X/X+4 DX

A: The given integral

Q: dr Vr - 9

A: Given: I=∫drr3-9   ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: dy of y3Dx dr Find csc2r,

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Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

Q: 1 x²y dy dx 2 Jo /0 Jo

A: Consider the expression is, 12∫04∫02x2ydydx Solve the integral as,…

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.