Luse integnal a stande substutuon to educe the 3(3x+12) dx,u= 3X +12 du 3,2 * du= 3,2dx

Q: sketch region 4 reverse order then evaluate i. the Integration (4 x +2) dy dx x 2

A:

Q: 8x + 5 Split the integrand I dx into two parts. 8x + 5 dx 1 - x2 8x dx + 1 - x2 V1- x2 2x 8x + 5 dx…

A:

Q: integration 1. Sx sec? 2xdx

A:

Q: 19x + 87x2 -) dx (Use Term by term integration) O (38x + 58) Væ + C O (38 + 58 /æ)V¤ + C O (38 +…

A: Given :                      ∫19x + 87x2xxdx

Q: egion in the first quadrant is bounded by the curve y=1+ sin²x, the coordinate axes and the line x==…

A: Topic:- application of integration

Q: stion 30 Complete the integration: Ssin (x)cos°(x)dx x sin (2x) sin³(2x) 16 32 Determine the value…

A:

Q: cot 2x Evaluate the integral dx . V cor²(2x) – 15 csc (2x) A ·Arcsec 8 + C 4 -- In |cot (2x) +…

A: The given integral is: ∫cot(2x)cot2(2x)-15dx Substitute cot2(2x)-15=t          ....(1) Fromm the…

Q: Prove that (arccsc x) dx d d %3D (csc-1 x) = %3D - dx Ju/Vu2-1

A:

Q: x' cos 2x dx

A:

Q: integral et sin (t-s) ds

A:

Q: sec 2x da 4. I+3 tanzx

A: Integration methods help to find the answer to the problem. Substitution of the function helps to…

Q: Integrate: oa dx. -00 8-x3

A:

Q: Integration by parts tan Cx) dx

A: Given- ∫extanxdx To Find- The value of the above integral.

Q: 1o. 1 |x-3|dx

A:

Q: Integration by Parts 1. L, Cos-1 x dx

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Integrate using substitution. Clearly state your substitution. 2 /          x^2 sqrt(1+x^3) dx -1

A:

Q: integration to find the general 3y? dy = (2x – 3) dx

A: It is simple integration.

Q: ((2- sec?x) emaie sec³x sec( 3A – x) In (ale) What should be the value of A for -dx to be integrable…

A:

Q: 2 csc x 11. Evaluate dx by using substitution method. (1– cot x)'

A:

Q: 6. Integrate , v4 – x² dx using trapezoids. Divide[-2,2] into 20 subintervals. Give the answer…

A: Given that, the function is fx=4-x2 and the value of a=-2 and b=2 and n=20. Note that, the formula…

Q: integral u du formula answer dx V3 + 2x – x dt VE (t – 9) sec?x V5 – sec²x dx

A: The given integral is As, So, the given integral can be written as Now, apply method of…

Q: Inteprete Show your work COS dx

A:

Q: [I sin(x/ y)dxdy Jo

A: We have to evaluate the integral…

Q: itegral 6ze dy dx dz

A:

Q: Vx In 2x dx=u v- v-fvdu Using Integration By Parts, Find Uv- du O 3 xVx In 23 2 12x- dx | O 2 Xx In…

A:

Q: Integration by parts is based on what formula?

A: Note that the product rule for differentiation for two functions fx,gx is ddxfg=gdfdx+fdgdx…

Q: Diffential Equation by Substitution:   DE (x+2y-1)^2 dx = dy

A: We have to solve differential equation.

Q: sin³ y dy 2. S 1- siny

A: Solution Given   ∫sin3y1-sinydywe need to find the integral

Q: cot xdx 3. J V1+lnsin x

A:

Q: Integration review Evaluate the following integrals.

A: ∫secθ+cscθsecθ cscθ dθ=∫secθsecθ cscθ+cscθsecθ cscθ dθ=∫1cscθ+1secθ dθ=∫sinθ+cosθ dθ=-cosθ+sinθ+C

Q: 2. dx 2. Solue integra

A:

Q: 1. Divide the interwal [0, t], t >o mto n Show that equal parts Jin x dx 1- Cost

A: Divide the interval in n parts and using left sum method solve the integral:

Q: c) tan³ x sec³x dx 3

A:

Q: 92?e-8-dz = %3D

A: Simple integration

Q: oints. SHOW YOUR WOR r(x) = %3D x+2

A:

Q: 2. f 3xe4 dx 2. S 3æet" dx

A:

Q: Reversing the order of integration: (2) O dy.dx- dx dy ........ O 2

A: Reversing the order of Integration : Consider a double integral over a domain D, the we can express…

Q: J arcsin vc da

A: To evaluate the given definite integral.

Q: ential equation (41 2) = %3D

A:

Q: Find the genera dx = x + y dt dy --2x - y dt

A:

Q: sin20 B)Evaluate the integrals: i) f/2 inzerdrde, ii) ¹/2 ¹/² finx ₂² siny dz dy dx . 0

A:

Q: 12 V3x 4e dx V3x Please evaluate the integral 3

A: In this question we have to find the Integration.

Q: Two methods a. Evaluate - dx using integration by parts. Vx + 1 b. Evaluate = dx using substitution.…

A: (a) Consider the provided integral, ∫xx+1dx Evaluate the provide integral by parts method. We can…

Q: 13. J sec0 de 14. J cot4x csc4x dx.

A:

Q: 2 What is /- dx? oJ-dx = -sin-x+ C %3D /I-x² • /-dx = 2sinx+ C %3D dx = -2cos-x+ C %3D oS- dx =…

A: We will solve the given integral.Below find the solution in image.

Q: dy Use implicit differentiation to find dx X+3 %3D У -3 3y = dy %3D dx

A:

Q: 6. f(In x)² dx

A:

Q: olve 2xy dx-(1-x)dy=0 using two different DE techniques.

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.