8. Use substitution, or a change of variables, to evaluate each definite integral ) V+2 p- a) 1-2dæ 0

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: In evaluating / (2x – 3) Vx– 2 dr by substitution, if 4 =x - 2 then what will be the resulting…

A: Given : Indefinite integral ∫2x-3x-2 dx   To find : Resulting indefinite integral by substituting…

Q: gralof 1/x from ac to bc (0<a<b) is the same as th

A: The purpose is to prove that , ∫ab1x dx=∫acbc1x dx The  integral of 1/x from a to b.…

Q: Evaluate the indefinite integral. 4 dt (t + 11)? + C

A: Integration of 4/(t+11)^2.

Q: Evaluate the given definite integral using appropriate substitution: 2xdx 2 ... © 3V2 ... © 4V2 3

A:

Q: Use a substitution of the form u = ax +b to evaluate the indefinite integral belov 7x+1 dx 7x+1 dx%=

A:

Q: ... Evaluate the given definite integral using appropriate substitution: 2xdx = O V2 ... (A) 3 3 B…

A:

Q: According to the guidelines in the text, what is the correct choice for u in the following integral?…

A: According to the given question it is required to choose the value of ‘u’.So, in the given integral,

Q: In evaluating JxVx-2 dr þy substitution, if u =x- 2 then what will be the resulting indefinite…

A: Explanation of the answer is as follows

Q: 4. Use properties of integrals to verify the following inequality: 4. /4 sin xdx s 24 24 VI

A:

Q: S)Use the Fundamental Theorem of Calculus to decide if the definite integral exists and either…

A:

Q: 2ェ dr Vェ? +1

A: We have to find the given integral.

Q: Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

A:

Q: In evaluating 2x – 1 dx by substitution, if 4=2x – 1 then what will be the resulting indefinite…

A:

Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

A:

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) 4t-5 dt. If the integral does not…

A:

Q: In evaluating J*Vx+2 dx by substitution, if 4 =x+2 then what will be the resulting indefinite…

A:

Q: In evaluating 2x -1 dr by substitution, if u =2x – 1 then what will be the resulting indefinite…

A:

Q: Next, integrate with respect to 0. T/2 1 e4 1 - de = 1. | T/2 1 - e4 Again, apply the Fundamental…

A: Here, all the parts are correct except part 3 of 6. The part 3 of 6 is: Evaluate: 12∫0π21-1e4dθ

Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: Use the method of u-substitution to evaluate the given integrals. 4t dt 2 – 812

A:

Q: evaluate the integral; ∫ [5,1] t/1+t^2 dt

A: We have to find the value of given definite integral. To find that we use integration by…

Q: 1) The following formula is entry #26 in our textbook's Table of Integrals. u? du ="Va" +u° -…

A: Given the integral ∫x225+x2dxWe need to use the formulae ∫u2a2+u2=u2a2+u2-a22ln|u+a2+u2|+C

Q: Evaluate the integrals ∫√(1 + cos (t/2)) dt

A:

Q: Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

A: integration

Q: In evaluating (2r+3)Vx+ 2 dx by substitution, if 4=x+2 then what will be the resulting indefinite…

A: This can be evaluated as follows:

Q: Use the substitution. 9 tan(0) to evaluate the indefinite integral 85dx +C J z²Væ² + 81

A:

Q: Evaluate the indefinite integral. dt (t +7) + C

A:

Q: Evaluate the integral, if it exists.  ∫01Sin (3 π t) dt

A: Given the integral ∫01Sin (3 π t) dt We need to evaluate the above integral.

Q: In evaluating x(4 – x) 3 dx, if we substitute that u=4-x, then what will be the resulting integral…

A:

Q: Evaluate the integral: 2e π/3 √√²² √²/³ t Inutans ds du dt

A:

Q: Evaluate the integral of sinº x dx from o to n/2. А. П/32 В. гп/17 С. зп/32 D. 5n/32

A: We know, 2sin2A=1−cos2A  2cos2A=1+cos2A2cosAcosB=cos(A+B)+cos(A−B)

Q: The value of the definite integral csc adx is 0 1 -1 1/2

A:

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. In 4…

A: We need to substitute e^t = x to solve it.

Q: Evaluate the definite integral. •4 ti + t?j| dt 3 |(7 - 1) 2 17 3 173 3

A: The value of the given integral is 1/3(173/2 - 1)

Q: 10. | Vi(1? + 31 + 2) dt

A:

Q: In evaluating x+2 dx by substitution, if 4 =x+2 then what will be the resulting indefinite integral…

A: We will evaluate this as shown below

Q: Show detailed solution for the following integral: (Non-anonymous questionO) S tan'z sec³z dz 7

A:

Q: 1. Use substitution to express each of the following integrals as a multiple of Sadu for some a and…

A:

Q: In evaluating /x V4-x dr by substitution, if =4-x then what will be the resulting indefinite…

A:

Q: In evaluating x+2 dx by substitution, if u =x+2 then what will be the resulting indefinite integral…

A:

Q: (b) Suppose we know that "(3/(x) – 2) dr = 6 and that af(a*) dr = 8. Use this information and…

A: The detailed solution is given below Thank you

Q: Evaluate the definite integrals: (a) / (v + dr = 2.x (b) ret“ dr = 2x +1 (c) / dr dx = (고2 + z)3

A:

Q: Choose the most appropriate answer: Evaluate the integral : f 7x6 dx x7+2 O In(x7+2) + C O In(x7+ 2)…

A: We will use substitution method to solve the integral.

Q: If h(u)du = 4 and .6 h(u)du = 4.4 what does the following integral equal? h(u)du =

A:

Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below

Q: Evaluate the integral in (7x) -dx. Choose the correct answer below. O A. - In (x) - 16 1 +C 16x* -In…

A:

Q: Use the specified substitution to find or evaluate the integral.

A: We have the given integral as I=∫et-3dt Let us consider that,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.