Q-4) Find the integration of function (f (x) = x2 + 1) by using "Simpson Rule" when (n=6) on the interval [0, 3]. %3D

Q: Evaluate the integral. (Use C for the constant of integration. x² 3/2 dx - 4x²)2 3 + 4x

A: We have∫x23+4x−4x232dx

Q: Q2.Use Triangular method of integration, find the integral f dx. √√x²-9 5x4

A:

Q: Find g(x) if g (x) = (30x² – 60x) - 75»²–15z² and g(0) = -3. Round any numbers to 4 decimal places…

A: We use substitution method

Q: Q5. Approximate the integral | Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and Romberg…

A: Given the integral ∫-11sin (2x)dx.

Q: 6. Evaluate: dædy Hint: Use dydx as order of integration.

A:

Q: If a population is distributed normally with mean 0 and standard deviation 1, then the probability…

A: Given function is f(x)=e-x22 Solution for part a:…

Q: 16. dx x√√16+x²

A: To find out the integration.

Q: a. Find the derivative of ln (4q^7 – 10) dq. b. Using the result of the derivative above and the…

A:

Q: 5. Solve using integration by parts f x² Vx – 1 dx. Show your solution.

A:

Q: A curve for which y" = x passes through the point (1, –1) with .3 a slope of . Find the value of…

A: Given- A curve for which  y"=x passes through the point 1,-1 with a slope of 32. To find- The value…

Q: -2x-1 dx

A:

Q: Solve the integral. x5 + 3 1. х?(x2 + 2х + 1)

A: Given that  The integral  Using the partial fraction decomposition find the value of the integral

Q: dx 2√√x + √x

A: Solution of given question is written in below steps.

Q: 9. f (x) = x² – 8x + 12 9. f (x) = x² – 8x + 12 Opens up/down: Vertex: Axis of symmetry:…

A: The quadratic function is a second-degree polynomial in which the highest power of the variable term…

Q: Q5. (a) Evaluate the integral using integration by parts rule if fx'sin' 2x dx (b) Express the…

A:

Q: b What value of a and b that minimize the integral : (x* – 2x²) dx a (Hint: Where is the integrand…

A: We have to find the value of a and b

Q: A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration…

A:

Q: 1 Sxsec - Svdu- Using Integration By Parts, >x tan x- u v- Find UV-

A:

Q: 19. x'dx √√5x² +4 -S

A:

Q: A soft ball is thrown up vertically in the air at to = Os from an initial height of 15m and with an…

A: The formula for the motion of the object with variable velocity and constant acceleration is . Here,…

Q: 6. f In² x dx

A:

Q: /Use Simpson rule to evaluate the value of integration F(x) dx for n 4 -1 6. 6. 825 8 F(x) -124 -52…

A:

Q: 02:- By using integration by part, find :- (Choose two only) 2-f Inx (x') dx

A:

Q: 30. Someone is doing implicit integration and has reached this point. Please do the next step (only…

A: The objective is to simplify the given expression

Q: Evalvate W (3x) - JEJds 8. %3D 6x+9

A:

Q: dx 9.S: х+x4/3

A: Given:      ∫1x+x43dx   Expand fraction by 1x43:        =∫11x3+1x43dx

Q: dx x+x4/3

A:

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: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

A:

Q: Che number ofunits in Z31[x] is

A:

Q: 2. Integrate the following function (a) analytically 3. I- fxe2* dx and numerically using n = 4 (b)…

A: First determine the integral using integration formula's. Then use the formula of Trapezoidal and…

Q: 00 (log r)4 1+x2

A: Let fz=log z41+z2 By residue theorem∫C1+CRfzdz=2πi∑Residues of f inside the contour. However,…

Q: IV. Integration by Part 1. | sin x sin 4xdx Scos cos 2x sin 3xdx 2. 3. (sin(In r)dr

A:

Q: 1 1-x Change the order of integration and then evaluate the integral: fx dydx X Jx-1

A: We draw the graph of the limits of the integration then we change the order accordingly

Q: 20. Using the conditions of Exercise 10, determine how long it takes for the jumper to reach 90% of…

A: Please mention the condition given in question 10

Q: Double of Integration of square root of 25-x²-y² with respect to x bounded by (0,3) and with respect…

A: The given integral is

Q: Calculate the integral. (Use C for the constant of integration.)   dx x   4x4 − 1

A:

Q: The full solution y is obtained by adding the complementary solution to the particular integral, y =…

A:

Q: Find f(x) if f'(x)= point -6xe and f(r) passes through the necessary. f(z) = %3D (Use capital "C"…

A: We will integrate the given expression with respect to X to find required function

Q: 11)By using Tabular integration solve the integral f x³ 2* dx A)Sx³ 2* dx = x³, In 2 2* 3x2 2* 2* +…

A:

Q: 1. SIn(x2 + 1) dx

A:

Q: 4-x (x+6)2 dx can be found by several diftevent methuds.Integration by parts yeilds 4-X dx = X-4…

A:

Q: Use Romberg integration to approximate √² 2x² + x − 1 dx. Compute the Romberg table until Rij-…

A: The Final diagonal element is always consider the best estimate of the integral  I=∫abf(x)…

Q: Use integration by parts to derive a reduction formula for x"e- dx. Jse the result from part 1 to…

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: Consider the indefinite integral of  S 3x^3+3x^2+5x-3/x^2-1 dx

A:

Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

A:

Q: (a) Evaluate the integral using integration by parts rule if x' cos' 2x dx (b) Express the…

A:

Q: Evaluate the indefinite integration. ∫?^3√(1+?^2)??

A: The indefinite integral of any function f(x)=p(q(x)) q'(x) can be evaluated using substitution of…

Q: dx 6. S (x2+6x+34)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.