∞ sin2x dx (x²+1)²

Q: What is the integrable form of sin-cos-sin0 do? 2 2

A: SOLUTION-

Q: Solve: The indefinite integral of the integrand (cos x/1+sin2 x) dx

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Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: sec 3x tan² 3x dx

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Q: Find the indefinite integral .

A: To find the indefinite integral  I=∫sin-12x1-4x2dx  Let u  = sin-1 2x dudx = 11-2x2du = 11-4x2 dx

Q: Evaluate the integral. ∫0 π/3 tan5 x Sec4 x dx

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Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: Perform error analysis of approximation derived (a) 1 x² 1 - at xo = 0 X (b) sin (₁) ₁ X- at x = = 0…

A: Given that: a 1x2-1 at x0=0b sin xx-1 at x=0c exp x2-1 at x=1 and x=-1 The objective is to analyse…

Q: Evaluate the integral. ∫0 π/2  Sin2 x Cos 2 x dx

A: Consider the given integral as Use the identity to solve the integral such that

Q: •3 sin (7|3 – 2x) dx

A:

Q: Determine if the integral * 1+sin² # dx is convergent or divergent.

A: We can determine if the integral ∫1∞1+sin2xxdx is convergent or divergent using comparison test.…

Q: [ cos² 2x sin² 2x dx

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Q: Apply the secant method to solve f(x) = e** In x² – x = 0. Discuss the procedure for dealing with…

A: We are given the following function.  f(x)=ex2lnx2-x=0. We have to solve by the secant method. Note…

Q: What is the integrable form of sin-cos-sin0 de? 2 2

A: A detailed solution is given below.

Q: Integrate (three) of th 1) f sin6x cos3x dx

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Q: Find the indefinite integral ∫tan3 x/2 sec2 x/2 dx

A: we have to find the value of indefinite integral  ∫tan3x2sec2x2dx let the given indefinite integral…

Q: Evaluate the integral f sin²x cos³xdx.

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Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: */16 etan(1r) sec2(4x) dr

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Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: Find the indefinite integral S (8x2/3 + 5* – cos(x))dx and verify the result by differentiation.

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Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: Compute the indefinite integral. ∫(1−sin2x)/(cosx) * dx

A: The given integral is,

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Find the definite integral of ƒ™/* cos 3x sin 5x dx. -π/4 Option 1: Option 2: Option 3: Option 4:…

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Q: 2. Apply appropriate trigonometric substitution to compute the integral 1-4x +2 dx /2x

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Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Calculate the integral ∫dx / sin4x+cos4x.

A: Given,   .

Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: Su+1 dn th-2

A: I =   ∫135x + 1x2 + x - 2dx    = ∫135x + 1x2 + x - 2dxWriting5x + 1  = A (2x + 1) +BOn solving , A…

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: This is exercise 26 of Section 7.5 page 460. Find the integral æ* sin(æ²) dx-

A: Answer is given in the picture

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: cos(9x) -dx COS J 1+ sin²(9x)

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Q: 14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint:…

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Q: Prove the following continuous time Fourier transform relationship. sin(at) 1 X(N) = Continuous Time…

A: Fourier inverse of XΩ=1    -π≤Ω≤π0    otherwise is : F-1XΩ=12π∫-∞∞XΩejΩtdΩ…

Q: What is the integrable form of sin-cos-sin0 do 2 2

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Q: Evaluate the integral. dx JSlx2 - 3 sin 1 33 x + C 3 sec1 |9x - 3| + C sec 1 19 x| +C * sec 13/5 x|…

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Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

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Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…