Q4) Solve the integral by Simpson's rule x3 cos2x dx, h 0.2

Q: How do I evaluate the indefinite integral?

A:

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

A:

Q: •2 dx

A:

Q: Solve the integral. sin x dx 10. cos2 x + cos x – 2

A:

Q: cos y dy sin² y + sin y – 6

A:

Q: Find the indefinite integral. ​ integral of sin^3(4x)*cos^4(4x)dx

A: Important points for the question: 1. sin2 x + cos2 x = 1   sin2 4x + cos2 4x = 1 2. ∫xn.dx =…

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

A:

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

A:

Q: 15. Use a suitable change of variables to determine the indefinite integral. [1²cos² (1³) sin(1³)dt

A:

Q: •3 sin (7|3 – 2x) dx

A:

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: Use the tabular method to find the indefinite integral. ∫x3 cos 2x dx

A:

Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Evaluate the integral. (Use C for the constant of integration.) cos3 sin2 dt

A:

Q: Verify the integration formula. S 6 sechx dx = tan-1 (sinh 6x) + C (A) No B) Yes

A:

Q: Solve the integral. sin x dx 10. cos2 x + cOs x – 2

A: Given: ∫sinxcos2x+cosx-2 Let u=cosx, thendudx=-sinx and dx=-1sinxdu.…

Q: Solve: The integral of (sec(x))^3 dx.

A:

Q: Find the trigonometric integral. (Use C for the constant of integration.) (cos(20))(sin(0) +…

A:

Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

Q: Find the indefinite integral. X cos 8TX2 dx

A: To evaluate the integral: I=∫x cos 8πx2 dx⇒I=∫cos 8πx2 x dx...(1)

Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan (x) sec®(x) dx C must be in…

A:

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: (1+ In²e) -' d® Otan-'(In®)

A: To evaluate:2) ∫41+ln2θ-1θtan-1lnθdθ

Q: Use integration by parts to solve the indefinite integral of [sin5xcos3x]dx

A:

Q: 2* csch (2*) dx J cosh(2*) – sinh(2*)

A:

Q: 12 cos6x. sin³ xdxCalculate "/2 3 the integral

A: It is integral problem.

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

A: Given,             ∫π40sin4tdt

Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

A:

Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

A:

Q: s/4 dx 2- 1+tanx 3.

A:

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

A:

Q: integral of (e^2x)(sin3x) using u=e^2x

A: Given, ∫e2xsin3xdx    We have to find the integral

Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Solve using an integral cos²(x) + 2cos²( cos³(x) .dx

A: Evaluation of the integral

Q: cos x dx

A: The given integral is ∫x2cos xdx We have to integrate the given integral using integration by parts

Q: use a geometry formula to find the exact value of the definite integral.  5 dx on interval[-2,6]

A: Question is to find the exact value of the definite integral 5dx in the interval [-2 , 6 ]It is…

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts: ∫sinn x dx=-sinn-1 x cos…

Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

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

A:

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

A:

Q: Select the basic integration formula you can use to find the indefinite integral. 10 dt (10t – 3)2 +…

A: Given that              ∫ 10/{(10t - 3)2 + 81} dt Here we have to find the indefinite integral by…

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|…

A:

Q: Use trigonometric substitution to solve the integral Jx*V1+x² dx

A: Note the results :     (Identity)

Q: Evaluate the integral. (x² + 4x) cos(x) dx Work must each include tabular method, OR u, v, du, dv…

A: =∫(x2+4)cos(x)dx Integrate by parts: ∫fg′=fg−∫f′g f =x^2+4, g′ =cos(x)   ↓ steps   ↓ steps f′…

Q: Solve the integration by parts | (x² – 2)cosh(x) dx .

A:

Q: Q3: Use integration by parts (Tabular method) to find the integral (r³_2 x² +3x +1) sin(2x) dr

A: The given integral is ∫x3-2x2+3x+1sin2xdx To solve the integral using by parts .

Q: Solve: the integrand (pi/3 sin5x) dx on the integral pi/2 to 3pi/2

A:

Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…

Q: Solve numerically the integral e**dx ´dx by: (1) Trapezoidal rule with n = 4 (ii) Simpson's rule…

A: The given integral is, 12π∫-22e-x2dx