1 Use the substitutions given to find fI+x dx; u = 1 + x + sin x dx; u = sin x cos x a

Q: Evaluate the definite integral.

A: Given : The definite integral is ∫π 3π 2  cos x ( sin x )sin2 x -14 dx .

Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

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Q: (23) If f(x) = sin zx, find the value of fe (x). 23 sinx %3D 23 e. sin x a. 23 b. cosx . 1 cos TEX…

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Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: EVALUATE 3 x2 +1 cos dx -1 dx x2 +1 А. cos В. О C. 2/ cos 3 dæ x2 +1 D. 1

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Q: 3 cos (x) sin (x) dx = %3D 2 15 O None 6

A: To find the value of given ∫0π23cos2xsin3xdx

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3r becomes u du. Select one: a.…

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Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

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Q: S sin 7x dx is equivalent to which expression? A S(1– cos²7x)(cos 7x) dx B. S(1 - cos'7x)(sin 7x) dx…

A: As per Bartleby guidelines we're supported to answer only one question when two or more different…

Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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Q: 13. For J* sin x dx, what is u? sin x dx 2x dx -x cos x+ 2x sin x+2 cos x +C Oc. OD.

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Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: (1 + cos 7t) 2 sin 7t dt

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Q: 2 Find the x-intercepts of y = 2 sin x + sin x – 1 on the interval [0, 27). %3D

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Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

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Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: 11. Find if y= cos(x) A. 2x sin(x) B. -x sin(r) 12. Differentiate: y=x cscx A. y' = cscx(1+x cot x)…

A: we have to differentiate the given equation . y=ex3

Q: find sin x cos? x dx 75. 76. sin 2x sin (cos 2x) dx er dx et + e* (e2x + e)² dx 77. 78. x + 1 e* + 1…

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Q: Evaluate f sin (3t) cos(3t) dt Select one: a를sin(3t) + C b. sin (3t) + C . 습sin"(3t) + C o 18 d. sin…

A: Given:

Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Eliminate the parameter t from the following. x = sin t − 3, y = cos t − 2

A: Eliminate t by squarring

Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

Q: * (s in-(x))² dx = V1-x2 Select one: а. sin-(x) + C 1 - x? b. (sin-(x))³ + C 3 C. sin-V1 - x²) +C O…

A: With the help of substitution method, integration is solved.

Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

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Q: Evaluate f sin (3t) cos(3t)dt COS Select one: sin (3t) +C a. b. sin(3t) +C sin (3t) + C d. sin (3t)…

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Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , Ɛs= 0.002

A: This is to be solved by successive bisection method.

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

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Q: sin(4x) cos (2x) dx = +(st)(9) (e) None sin sin (con (2x) Cos сов (10х) sin (2x) sin (10x) (e)( (Cо…

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Q: B sin 5x+ sin 3x 1 sin 5x+-sin 3x+c 6 I 10 fcos 4x cos.x dx = ?

A: Given :∫cosxcos4xdx

Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

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Q: Use graphs to evaluate 2π S 2r S 0 sin x dx = cos x dx = 2t S 0 2π sin x dx and cos x dx. 0

A: We will find the required.

Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: . Evaluate [10x cos(x²) dx . A) sin(x³)+C C) 30 sin(x') +C 3 B) sin(x') +C 10 D) 3 sin(x') +C 10

A: Our Aim is to evaluate the integral given below:-∫10 x2 cos (x3) dx -(i)

Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

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Q: 3 The value of (Isi n(x)| + x²) dx is .a 2 f(- sin(x) + x²) dx 0 .b .C 2 f(sin(x) + x²) dx -3 .d 3 ,…

A: Let's find.

Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

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Q: | 10(2 sin(x)) cos(x)dx if J Ax)dx = 13

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.