dx 16 — х2

Q: q dx (6x²+ 32) dz

A:

Q: Compute the indefinite integral, and demonstrate that your solution works by differentiating:…

A: Since you have asked multiple question As per our policy , we will solve the first question for you.…

Q: Find the indefinite integral using the substitution x = 4 sin θ.

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Q: Use the Method of Substitution to find the indefinite integrals: a) / te“dt (q

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Q: 1 sin Tx cos TIx dx 0,

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Q: 8 x3 dx Vx2 + 36

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Q: Evaluate the definite integral: J 7 cos (2x + 7) dx Note: Round to the nearest tenth.

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Q: View Image for problem

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Q: Evaluate the indefinite integral: ∫ cos t cos(sin t) dt

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Q: tan 5v sec 5v dv

A: Consider the integration  I=∫tan 5v sec 5v dvOrI=∫sin 5v cos25vdv

Q: use the method for odd powers to evaluate the integral.

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Q: Evaluate the following indefinite integral. Use C for constant of integration. * cos(10x) + sin(20x)…

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Q: Find the indefinite integral

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Q: Find the indefinite integral- cos t dt sin t

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Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

Q: So 2"dx.

A:

Q: Find the indefinite integral using the substitution x = 2 tan θ.

A: Then integrate with substitution

Q: Evaluate the indefinite integral sin (t)cos (t)dt

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Q: Use substitution to find the indefinite integral

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Q: Evaluate the definite integral.

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Q: 2r cos x dx

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Q: Evaluate the definite integral. 1 ex dx 0 1 + e²x JO

A: We will solve the definite integral.

Q: 15 – 5 sin (z) ) dz

A: To solve the given indefinite  integral.

Q: Find the indefinite integral and check the result by differentiation.

A: Consider the given expression as dydx=4x+4x16-x2

Q: Find the indefinite integral f Vx2 – 6x + 5 dx using an appropriate trigonometric substitution.

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Q: sin2(0) cos(0) d0, sin(0)

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Q: Evaluate the integral I sin(x)e-" dx.

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Q: Use a table of integrals to evaluate the definite integral.

A: Let the given integral be y - y = ∫012x3ex2dxy = ∫01x2ex22xdxLet,t = x2Differentiating on both sides…

Q: Find the indefinite integral by making the substitution x- 7tan e. dx 49+x²

A: See attached file for a step by step explanation.

Q: Find the indefinite integral. x' + dx +C.

A: Integrate

Q: Evaluate the indefinite integral. 3e* sin(e) de

A: Solve the integration by substitution method

Q: Find the following indefinite integral. I dx x2 + 9

A: From the given problem:   I=∫xdxx2+9...(1)   Let,   x2+9=t   To differentiate with respect to x.…

Q: cos (78) dx, u=7

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Q: Determine the following integral by making an appropriatesubstitution.

A: Given∫cos3x2-sin3xdx

Q: Evaluate the integral using an appropriate method. T/3 x sin(3x) dx

A: ∫0π3x sin(x)dx

Q: Evaluate the integral, if it exists.

A: Given- ∫-11sinx1+x2dx To find- The value of the above integral. Concept Used- The above integral can…

Q: Find the indefinite integral.∫(cos5 t/√sin t)  dt

A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

Q: Evaluate the definite integral on the interval [0, pi/4] sin(t) / cos^2(t)  dt

A: By substitution, we calculate the value of given integral.

Q: Compute the indefinite integral. - sin z dx COS X Answer: + C

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Q: Find the indefinite integral using the substitution x = √x√4 + x² dx + C 2 tan(0)

A: SOLUTION-

Q: Evaluate the definite integral. t10 sin (t11) dt

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Q: Evaluate the definite integral integral from 0 to square root of pi  xcos(x2)dx

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Q: Evaluate the indefinite integral.

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Q: Find the indefinite integral. cos t dt sin t

A: Consider the given indefinite integral, ∫cos5tsin tdt use the trigonometric identity, cos2x=1-sin2x…

Q: Evaluate the integral.  integral sin 9  x  dx

A: Given ∫sin9xdx

Q: Determine the following indefinite integral. dx |( + x7) dx= O

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Q: Evaluate the definite integral 15 cos(t)dt:

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Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ

Q: Find the indefinite integral by using the substitution x = 4 tan(0). (Use C for the com 4x2 dx (16 +…

A: on solving this we get the

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.