Vsin x.cos x 1+ 2.ln x 3y (аns.: 4

Q: dx Perform the Integrations 1+ sin x+ cos x

A:

Q: TC 16. Evaluate the definite integral cos2 (4t –) dt

A: 16. Now,

Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1 To evaluate the integral dx, we (x2 + 2x)3/2 sec 0 1 substitute

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: Evaluate (3 t + 5) cos () d+ using integration by parts .

A:

Q: dy - år if y = In (sinh 50) and x = cosh 40 dx

A: Solving the problem by doing the derivative.

Q: 1/2 2. Approximate the integral: 1 - cos(2x) dx within an error of 0.01. x2

A: According to question given that∫0121-cos2xx2dx within an error of 0.01

Q: The suitable substitution to evaluate the integral V cos (2x) dx is COS

A: Given that:∫cos5(2x)csc3(2x)dx

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: dy 11. = cos(In z) dx

A: The given data is: dydx=coslnx  To solve the differential equation.

Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

A:

Q: A-Evaluat wing integrais: 1) S (cos x / sin? x) dx. 2) S (2x+4)/3 dx, use x-0 to x=2. 3)…

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Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

A:

Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: 8. Evaluate the double integral. cos 2x.sin y dy dx

A: Solution-

Q: !!! 6 cos (x2) Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Triple integral

Q: Compute for the arcsinx dx . Which of the following is not an antiderivative of the function f(0) =…

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Q: 5) S V2 + sin 3t · cos 3t dt

A:

Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: J (5x)sin( nn : 1.5 )dx + , (5x – 15 )sin NT X 1.5 dx 1.5

A:

Q: 10 a) Evaluate x cos(5x) dx by using integration by parts.

A: Given:

Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: I need solution to this problem.

A:

Q: A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og ys x*

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Q: Solve the following integrals: i. S(e** cos(2x)) dx using integration by parts or tabular method.…

A:

Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

A:

Q: /16 cos (16л x5) dx dy. Os xs 2 Os ys x*

A:

Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: evaluate using Integration by Parts.

A:

Q: 2х n evaluating J cos²(2x) Tx using integration by parts, identify the portion of the integrand to…

A:

Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: ons z = sin y arn

A:

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

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Q: 2.2 Evaluate following integrals. .sin VT cos E 2.2.1 dx

A:

Q: Q1: Find the integration of : (choose 3 only ) 1. Sc (3 sin x)cos (4 sin x). cosxdx Cos

A:

Q: 1. Perform the integration. Show all necessary solutions. 8t² + sin t sint + cos ty dt co t

A: Find your answer below

Q: The definite integral from 0 to = of cos x sin xesin² x dx is 4 O e - 1 e+1 e-1

A:

Q: 0.5 COS T - In(4 sin z) dz. J0.1

A:

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu

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.