Q1: Evaluate the folowing integrals by using a substitution to reduce it to जकंन standard form: (i) - dr (ii)} sec²x dx (ii) dx tan x

Q: Find the general indefinite integrals integral of x(x3+2)2dx integral of 3x2(x3+1)4dx

A: The given integral of  xx3+22dx     =    ∫xx3+22dx = ∫xx32+2(x3).2+22dx  = ∫x7+4x4+4xdx =…

Q: x arcsin(x²) dx;

A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

Q: JxVx-6 dx cos(x) dx sin(x)+2

A:

Q: What are the new limits of integration if apply the substitution u = 6x + n to the integral sin (6x…

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Q: ) Use integration by parts to verify the reduction cosxsin x n-1 Scos" xdx=!

A: Here I=∫cosndx ⇒I=∫cosn-1x×cosx dx using integration by part;

Q: Evaluate the integral using formula was (from the 1page differentiation & integration formula) by…

A: Hint : 1. Use substitution : ex = t. This integral will turn into a standard Integral.

Q: Sketch the graph the integrands and use areas to evaluate the integrals. | Ix| dx -2

A: Follow the procedure given below.

Q: Show that arctan(Tx) – arctan(x) -dx In T. by first expressing the integral as an iterated integral.

A: To show

Q: Find the indefinite integral using any method ∫ (3x3 + 4x) /(x2 + 1)2 dx

A: We have to evaluate

Q: Use any method to evaluate the integrals ∫ 2x - 2-x/2x + 2-x dx

A:

Q: What are the new limits of integration after applying the substitution u = 5x + z to the integral s…

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Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

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Q: Use the properties of integrals to verify that 2 < (', VT+x² dx = 2/7 without evaluating the…

A: Please examine the graph of (1 + x2)1/2 below:

Q: nich integral represents the length of the graph of y = In(1 – x²) over the interval [0, ]:

A: here option A is true because length is given by =1+(dydx)2dx so here…

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: CSCX-1

A: Multiply numerator and denominator by (cscx-1)

Q: 9. f(x³ - 4x)dx -3 (x²-1) dx 10. ₂

A: We have to find the integral

Q: Evaluate a. Fв- x-3Dаx

A:

Q: Use the tabular method to find the integral. (Use C for the constant of integration.) 3x3 sin(x) dx

A: The given integral is ∫3x3sin x dx. ∫3x3sin x dx=3∫x3 sin x dx ddxxn=nxn-1∫sin xdx=-cos x+C∫cos…

Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: Find the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of…

A: We need to evaluate integral.

Q: 2. Describe how to deal with the singularity in the integral if one wants to evaluate this integral…

A: Given integral is  ∫01x-12e-x2dx           (i) Let fx=x-12e-x2 Clearly, x=0 is a singular point of…

Q: Express lim {5(x;)* – 6 tan°(x;)}Ax, n-+00 definite integral over the interval [-3,2n]. as a

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Q: Use Trapezoidal Rule with (n- 4) to find the integral dx x-1

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Q: Use reduction formulas to evaluate the integrals ∫ 2 sec3 πx dx

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: What is meant by indeterminate integral

A: Definition: An improper integral is the limit of a definite integral as an endpoint of the…

Q: 8x + 3 Break the integral into two integrals. Use a u-substitution on one and Integration Tables on…

A: let I=∫8x+3x2+1dx

Q: Q3: Use integration by parts (Tabular method) to find the integral (2³_2 x² + 3x +1) sin(2x) dr

A:

Q: sinx cos

A:

Q: (x²-5)dx x3+15+12

A: Use partial fraction concept  And integration (1/x)dx=logx , integration 1/(x²+a²)…

Q: Pls kindly help evaluating integrals by first differentiating Theorem Intergal(0,infinite)…

A: I am going to evaluate the given problem using the first differentiating theorem which also the…

Q: V1- cosxdx COSX

A:

Q: Compute the indefinate integral. integral (1-sin^2(x))/cosx * dx

A: Consider the given integral.

Q: | de P8- メレー Oe dedx

A:

Q: solve the integral: I2=  integral limit from 0 to 4= 1/((x+1) squar root of 2x+1) dx

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Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

Q: ( sin' x cos³x dx

A:

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: Use the basic integration rules to find or evaluate the integral

A: Given: I=∫1eln2xxdx for evaluating given integral, we substitute  ln2x=t…

Q: Find the integral of * dx J 2 sin x – cos x tan + 2 + V5 + C tan+ 2- V5 V5 |tan + 2-V5 V5 In tan+ 2+…

A: Option 2 will be correct choice.

Q: Use integration by substitution and the Fundamental Theorem to evaluate the definite integral. 2 |…

A: Use substitution method

Q: Find the indefinite integral by making the substitution a = 6 sec 0. 2-36 dx -1 6 C. Vx2 – 36 + 6…

A: Given

Q: Evaluate the integral using an appropriate method. [15 15 cos²x sin³ x dx

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Q: What are the new limits of integration if apply the substitutior u = 6x + t to the integral sin (6x…

A:

Q: 2 dax (x³-5)3 5)3

A: Please refer the attached image for complete solution.

Q: Evaluate the integral of 3(sinx)3dx using lower limit of 0 and upper limit = pi/2.

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Q: Use integration by parts, together with the techniques F, G Qof this section, to evaluate the…

A: Use integration by parts, together with the techniques F, G Qof this section, to evaluate the…

Q: integral of sec^4 (x) tan^2 (x) dx

A: Definition used -                                sec2x=1+tan2x…

Q: Find the indefinite integral.

A: