Evaluate the indefinite integral: 3 3 x² dx + С. x3

Q: calculate the integral in terms of the inverse hyperbolic functions.

A: We know that

Q: (d) | Ta2 – 4)3 dx -

A: To Determine: Convert the indefinite integral into definite integral using the interval [0,1]…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 4 dx (1 –…

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Q: Express the integral in terms of the variable u, but do not evaluate it. re21 In x - dx; = In x e5…

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Q: Find the indefinite integral.

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Q: Evaluate the indefinite integral. V 4 + x² dx = C %3D

A: Consider the integration  ∫4+x2dx

Q: Evaluate the indefinite integral:  ∫ z2(z3 + 1)12 dz

A: Substitute u=z3+1,du=3z2.

Q: Use properties of the indefinite integral to express the following integral in terms of simpler…

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Q: Evaluate the indefinite integral. V 16 +x² dx %3D to

A: We need to integrate ∫16+x2x4dx

Q: Use the substitution u= x² + 6 to find the following indefinite integral. Check your answer by…

A: Given, ∫2xx2+66dx and u=x2+6 ⇒du=2xdx Following formula is used- ∫xndx=xn+1n+1 ddxxn=nxn-1ddxa=0

Q: Evaluate the indefinite integral by using the substitution u = 6-x* to reduce the integral to…

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Q: Rewrite the integral using substitution: 3 ₁³ (x² cos(4x³)) dx

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Q: Evaluate the integral or state that it is "divergent" -5 х — 2 dx х2 +x — 6

A: From the given problem: I=∫15x-2x2+x-6dx So, we can also write as:…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 8. dx : (1 –…

A:

Q: Find the indefinite integral by using the substitution x = 8 tan(0). (Use C for the constant of…

A: ∫8x264+x22dx take  x=8tanθ dx=8sec2θ dθ =∫ 8(8tan(θ))264+8tanθ22·8sec2θdθ =∫…

Q: Evaluate the indefinite integral given below. [6e¹tan (2) Gett 6e4 tan (2x) sec² (2x) dx

A: The given integral: ∫6e4 tan2xsec22xdx

Q: Evaluate the Integral using the following values. [°x³ dx = 260, [°x dx = 10, [°dx = 2 [°(22-7x-x²)…

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Q: Find the general indefinite integral using definition. х5 + 3х — Vx + dx X.

A: we need to evaluate the integral,∫x5+3x-x+1x dx

Q: (c) dx 1 – x2 (d) | Va? + x² dx

A:

Q: Use substitution to find the indefinite integral

A: Given ∫1xlnxdx

Q: calculate the integral in terms of the inverse hyperbolic functions.

A:

Q: Evaluate the integral using appropriate substitution: (ii) x^2√(1 + x)dx

A: Let the given integral be y - y = ∫x21+x dx         ..................(1)Let,u2 = 1+x…

Q: Find the integral by algebraic substitution: ∫dx/√1+4x

A: In some cases integrals can be simplified to standard integrals by using an appropriate…

Q: Evaluate the definite integral two ways: first by a u-substitution in the corresponding indefinite…

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Q: Evaluate the Integral using the following values. -206 [³x² dx = 260, [°x dx = 10, [° dx = 2 (22-7x…

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Q: Determine the indefinite integral below. 3x 7 e + Vx' dx -7e 3x dx = +.

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Q: 2x (x+2)-5 dx z

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Q: Evaluate the indefinite integral by using the substitution u =x° +x to reduce the integral to…

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Q: (e) / V1 + x² dx (f) x² + 4 dx

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Q: Find the Indefinite Integral. (R 1 dx XV 4x + 81

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Q: Find the indefinite integral. (Use C for the constant of integra -8 + 12 dx ャ

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Q: Determine the indefinite integral J csch 2x dx.

A: To evaluate: ∫csch2xdx Let t=2x dtdx=2dt=2dxdt2=dx Integrating the given integral.…

Q: ²) S₁₂ x ² √ x²+1 dx St 2)

A: The given integral is; I=∫07xx2+13dx   ....(1) As we know the Power Rule: ∫xndx=xn+1n+1+C

Q: (e) / 3. (c) (Зх — 5)3 dx (d) / ((V– 5)² – x)² c - -

A: (c)

Q: calculate the integral in terms of the inverse hyperbolic functions.

A:

Q: Find the indefinite integral z(3 +z) dz.

A:

Q: Evaluate the indefinite integral. V 9 + x² dx %3D

A: ∫9+x2dx

Q: Use the substitution u =x +3 to evaluate the indefinite integral below. dx

A: Given Data: Integrand: ∫2xx2+35dx Substitution: u=x2+3 ......1 The derivative of equation (1) with…

Q: Evaluate the indefinite integral given below. 4e4/z² dx

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Q: Use the substitution u = x + 8 to evaluate the indefinite integral below. dx Write the integrand in…

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (18x – 17)°…

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Q: Evaluate the indefinite integral. 1+(Vx) dx Ti(5+ x)

A: The objective is to find the indefinite integral.

Q: Evaluate the indefinite integral. 1 dx x2 + x %3D +C.

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (9x – 8)° dx…

A: We need to evaluate: I=∫9x-89dx by using appropriate substitution. This can be evaluated as follows:…

Q: Evaluate the indefinite integral using u substitution  x^6sin(x^7) dx

A:

Q: Use the substitution u = 7x +x to evaluate the indefinite integral below. dx Write the integrand in…

A: ∫(14x+1)7x2+xdx

Q: Use the Method of Substitution to find the indefinite integrals: t3et“ dt dx x VIn x

A: The given integral,a) ∫t3 et4 dtb) ∫9xln x4dx

Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral below. V3x +2 dx

A:

Q: evaluate the integral from 0 to 3, x^3 dx/ sqrt 9+x^2

A:

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.