4). S§ dx (Improper Integral) Jo x-4

Q: Evaluate the double integral S S (11a°y³ + 11eš")dædy

A: We have to evaluate ∫36∫2611x3y8+11e5x dxdy   We evaluate this double integral using iterated…

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)2

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Q: Evaluate the integral. 6. 9 In(y). dy Vy J4

A: Given,             ∫49lnyydy

Q: 1. Evaluate the integral dx Jo x2 + 4x + 20

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Q: 7. Evaluate the Integral S (x + 3) dx

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Q: 2. Compute the following definite integral: X-3x+2 dx x2-2x

A: The solution is :

Q: Consider the following integral: (³ In(2x) dx.

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Q: The following improper integral (7x-5) dx (x+3)(x²-x+1)

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Q: in S 0 n soo

A: Here we have to Evaluate the double integral

Q: Evaluate the integral : S 8г2 +10х—6 (х—1) (х+1)2 dx = |

A: The given integral is ∫8x2+10x-6x-1x+12dx.

Q: s(s - 1)° ds

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Q: 24 Use properties of integrals to evaluate S (2x – 1) dæ,if 3 11 24 S (2x – 1) dæ = 104, and f (2x –…

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Q: S 3 7 39+x² dx

A: We need to solve integral.

Q: 3. Evaluate the following improper integral; -2 2 dx x² – 1

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Q: Evaluate the following integral. S 7. dz 25 16

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Q: What is the integral of e^(3.4*x) from x=1 to x=6?

A: Solve the definite integration and put the limit.

Q: Solve the integral: A In/1+ B -In|1+ x 5. 1 3X + C + C 5 x X + X x dx

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Q: Evaluate the integrals in ∫8 e(x+1) dx

A: ∫8ex+1 dx Put  x+1=t⇒1+0=dtdx⇒dx=dt

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)² 8.

A: The value of the integral ∫-∞02xdxx2+812 is given by: ∫-∞02xdxx2+812=-1x2+81-∞0=-181-1-∞=-181-0=-181

Q: Evaluate the double integral S' Sí a³y²dxdy..

A: Given that double integration and we solve it by using general property of integration. Here i…

Q: 3. Evaluate the integral fx?x* + 4x + 3) dx

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Q: Evaluate the integral.

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Q: Evaluate the indefinite integral. 3 dt (t + 8)5 + C

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Q: The following improper integral S (7x-5) -dx (x+3)(x²-x+1)

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Q: Evaluate the integral.

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Q: Evaluate the integral: S(6 + 5x) dx dy 22 44 O 4 O 2

A: Double integration

Q: the integral S(x³ – 2x – 1)e-*+1dx is equal to:

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Q: 1. (a) Prove the following. | (In x)"dx = x(In x)" – n (In x)-' dx

A: To prove that 1.a. ∫lnxndx=xlnxn-n∫lnxn-1dxb. Using 1.a compute the following      ∫lnx3dx

Q: Question 5 5. Use the fact that +C to either evaluate the improper integral dz, or show that it…

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Q: In 13 Iny ex+y dx dy. Evaluate the integral 1

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Q: Evaluate the following integral. e 4 ( In x) 3 -dx X 1

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Q: 57 Evaluate the integral |[xy dy dx. 12

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Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: z'e? dz

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Q: Evaluate the integral: Só(5 + 4x) dx dy O 18 O 36 O 2 O 4

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Q: Evaluate the integral x(x® –4) dx 1. O 1 10 (xº – 4)" +C 50 O 1 +C 60 10 +C 10 x° ( x7 -4x +C 6 7

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Q: fx'e* dx ets

A: To evaluate:                     ∫x2 ex3 dx

Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: Evaluate the following integral. Question 16 dx 7- Vx 9.

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Q: Evaluate the integral: S dx (x+6)(x-4) ← +C

A: Given problem:-

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: Calculate the following integral 1 Yez? - dædy 1

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Q: S √x²-a² X dx

A: To solve the given integral.

Q: Evaluate following improper integral: t+1 4- 12 0.

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Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

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Q: 4. Evaluate the following integral fel e(-²²-25) dt

A: Note:-  ∫ e-x2 dx=π2 erfx +C   Given integral is ∫0∞ e-t2-254t2 dt

Q: 9. In evaluating the improper integral dx , which of the following is true? (1-3x)2

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Q: 23: Evaluate the integral of ſ (5y+7) 5 dy

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Q: 8) The integral |4* dx is equal to 5x 5x 5x - +C C. In 5 А. -+C In 4 В. +C 5in4 D. +C 4 In5

A: Given ∫45x dxSubstitute u=5x → dudx=5→dx=15du=15∫4u duNow solving ∫4u duApply Exponential rule: ∫au…