I. Power Formula sec² xdx 1. S (1–4tanx)7 (2x+1)dx (x+2)*(x-1)* 2. S;

Q: T/16 23) "" (1 + etan 4x) sec2 4x dx

A: Topic = Integration

Q: S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x…

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Q: 6. |x²e-2*dx

A: Solved below

Q: 6x+13 1. Sx²+5x+6 - dx Co² (²) du

A: Dear Learner,We expert are following bartleby expert guidelines to answer the Questions. In case of…

Q: „T7/12 (1 + etan 3x) sec 2 3x dx Зе

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Q: 3/2 x+3/2 x² - 2 Show that dx = In 3.

A: Since there are multiple questions posted, we will answer the first question posted (4). If you want…

Q: ) Find the nearest distance from the point (-4,2) and the line 2x - y = 5 d²y and dx dy O Find if x…

A: 1. A) given point is (-4,2) and the line 2x-y=5 B) given that x=sin3z and y=tan23z find dydx and…

Q: 2 [(3 sec2 x + - x)dx 4

A: Integrate

Q: ,2 3 csc- x dx 1. /1–4cot2.

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: 7). S x² sech x³ dx

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Q: 7 49 – x² dx 2. Compute the value of

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Q: b) S (7x² – 5x² – 4)sin (3x) dx |

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Q: 0 xsin2x x² + 3 -dx =?

A: Given: ∫0∞x sin2xx2+3dx

Q: What is the solution of 5 |x - 2|dx

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Q: Find two numbers a and b with a ≤ b such that has its largest value. (10 + 3x - x²) ¹/3 dx

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

Q: (a) S v16 – 9x²dx using th - (b) dx using thes V9-x2 dx using the subs

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Q: 7). Sx² sech x³ dx 3

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Q: 32x ) dx In|xl + C 3 %3D - |- 3x. 2 In 3

A: let the missing term is Y

Q: 1 7) So dx V36- x2

A: Solution of the problem as follows

Q: _3. lim (17x – 4) х--18 А. -140 В. 310 С. -310 D. DNE

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Q: Find the y' and y''. y= square root of 1- sec (t)

A: Consider the provided function, y=1-sect Find the first and second derivative of the function. Now,…

Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: f(x)=4e+ sec x – 2x° +27x

A: topic-derivative of a function  note-As per our guidelines i  supposed to do only first question…

Q: 7rebz dx = 2 Your answer should be in exact form.)

A: Given integral to evaluate ∫-227xe6xdx This can be integrated using the rule ∫u·vdx=u∫vdx-∫u'∫vdxdx

Q: A) Find the nearest distance from the point (-4,2) and the line 2x-y 5 dzy dy and dx B) Find if x =…

A: A) The nearest distance from any point to the line is always a length of the perpendicular from the…

Q: A) Find the nearest distance from the point (-4,2) and the line 2x - y = 5 d?y dy and dx B) Find if…

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Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: 3. f10x-sec(5x) tan(5x²)dx ans : sec(5x²) +c (VF). cot 4. dx ,note: Vx = xr ans : 2 In

A: ∫10x·sec(5x2)tan(5x2)dxlet u=sec(5x2)du=sec(5x2)tan(5x2)·10x  dxdx=dusec(5x2)tan(5x2)·10x Replace dx…

Q: •3 sech? x tanh x dx 2

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Q: 3), x²e2* dx Ans. 20 (5e* – 1) Se4 4

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Q: 1-3x dx Jo J2x-3x² 4. 2х— Зх?

A: Given problem is

Q: b. Find S 5x*(x5 – 1)dx using a suitable substitution.

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Q: 9. -1 2x xe dx

A: We have to find out solution of integral

Q: 2x?+9х-1 1. S x(x2-1) dx

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Q: (a) f(x) dx = Enter an exact number only. 4 (b) |(4f(x) + 10x)dx = Enter an exact number only. 4

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Q: 4-x2 C. ye arccos

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Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: Evaluate the integrals

A: Given integral, ∫π23π41-sin2x dx

Q: dx lim dx %3D

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Q: 5. St? V1- t dt (2x+3) dx 6. S (x2+3x-6)

A: Please see the answer below.

Q: 2. Sin 2x dp X UIS 6.

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Q: ∫[(1/ (x2√(4 - x2))) dx] Please show all work

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Q: ' 7 cosh (x) dx = 1

A: We have to evaluate the integral ∫197coshxxdx

Q: (3) S 4-x² dx

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Q: 1- S 9-4x2 dx 2 - x tan- x dx

A: 1.Given integral,               ∫9-x2xdx

Q: 5 dx is: V4-x2

A: Given:  Let I=∫54-x2 dx To Find: To evaluate the given integral.

Q: Solve f 8x cos(7x) dx using Integration by Parts.

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Q: 21 (b), dx -1 3e2x

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Q: 5 |V25 – x² dx Compute the value of

A: Given: I=∫0525-x2dx we know that ∫a2-x2dx=x2a2-x2+a22sin-1xa+c                                  ...1

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: