2dt tv4t4 – 1

Q: CztsecxJ

A:

Q: (3t² – 4t + 7) dt

A: Given problem is :

Q: 1 xp x7 – x

A:

Q: +9 =zxe %3D

A:

Q: Evaluate the integrals

A: As per company guidelines, I can solve only one question.

Q: Evaluate the integral.   ∫  (4x7 − x−7 + 1)dx   =____________________+ C

A: Useful formula: ∫ xn dx = x(n+1)/(n+1)    +     C

Q: Evaluate the integral. xp xs 45 2. O 135 O 90 405 2. O 000

A: Definite integral

Q: Evaluate the integral. + 5v7 dv

A:

Q: 1 c) 1+4x2 dr.

A: See the details solution in below

Q: Evaluate the integral. | In(10 r – 9) dæ + C

A:

Q: V4 +x? xp

A:

Q: 3. (In x) –dx dx k) xVln x evi xp-

A: We know that integration of xn   =  xn+1/n+1. And we know that derivatives of d(lnx)/dx =   1/x.…

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the following triple integral: 3 x x 6z dzdydx

A:

Q: Evaluate the integral SSRe-(²*+y°)dA, where R is given by x? + y² 0. е

A: We will answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 12sin3xcos7x dx

A:

Q: Evaluate the integral. 2t + di

A: We have to find the integral

Q: Evaluate the integral of 2e2xdx from 0 to 1

A: Our Aim is to evaluate the integral given below:-∫012e2x dx -(i)

Q: f314+ 2xck

A:

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A:

Q: Evaluate the integral frever se 2. SS ー2 SinXy dsdx メ

A: Here we are given the following region of integration: The first part of region represent: x = y…

Q: dr V9+ 8a-a2

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

Q: Evaluate the following integral. +2dx

A:

Q: express each integral as a single integral.

A:

Q: Evaluate the integral. 3 x² + x + 1 xp lo (x + 1)²(x + 2)

A: To find:-   Method:- we use partial fraction method

Q: V3 d) dr VT² + 1

A:

Q: 1 | x(x² + 2)³dx

A: Given, ∫01xx2+23dx  We have to evaluate integral using u-substitution.

Q: Evaluate the following integrals. ∫8te7t dt

A: Given:∫8te7t dtIntegration formula:∫u dv=uv-∫v du

Q: d csinx 1 dt dx '3 1-t2 V5 t vt2 +1 dt Si Vx V1+ xVxdx

A:

Q: 9. dt 2 -4

A: ∫9t2-4dt=9·∫1t2-4dtLet u=\arcsec12t=9·∫secudu=9lntanu+secuSubstitute back…

Q: Evaluate the integral. xex . (1 + x)2 xp

A:

Q: Evaluate the integral * (2* – 4)" de by making the substitution u a6 – 4. - + C

A: We know that  ∫xndx=xn+1n+1+C We make the substitution u=x6-4du=6x5dxdu6=x5dx

Q: Evaluate the integral da (7x + 10)2" by making the appropriate substitution: u = dx (7x + 10)

A:

Q: Evaluate the integral. 2 vA + 4v8 v5 dv

A:

Q: Evaluate the integral. 4x2 - 3 da: J (32 – 2)(x² + 4) +C

A:

Q: Evaluate the integral. | In(9 x – 8) da +C

A:

Q: Evaluate the integral. 63e V7x 2 /x xp

A:

Q: 1.4. V9* + 25 de

A:

Q: 15. S(x + 2)²dx

A: Solve the following

Q: Evaluate the integral: /V13 – 49a*dæ

A: Integration

Q: Use the substitution technique to determine the following integrals:

A:

Q: Evaluate the integral 49 by making the substitution u = x* – 2. + C

A:

Q: Evaluate the integral of the following using Miscellaneous Substitution dx 4. Sa

A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: 20 + S 2c + 5 こ

A:

Q: Evaluate the integral. 2. v3 + 9v6 dv

A:

Q: Evaluate the integral: V100 – 2°dæ + C

A: The integral for the complex integrand can be solved by simplifying the integrand. The integrand can…

Q: Find the integral. хебх (6x + 1)2 xp

A:

Q: Determine the integral by making an appropriate substitution. et6

A:

Q: SxVx? – 9dx

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.