The power (P) supplied to an electric circuit is g ok (2t/® ¿2 dt . If i =41 * I sin(wt) , I is the curre 2n Jo frequency and R is the resistance, evaluate

Q: 1. Evaluate a) for²dr, 2. Evaluate fr+7r² dr. 3. Evaluate a) fe²dr, r/2 4. Find sin rdr. b) dr, c)…

A: 1. evaluate  a) ∫01x2dx = [x3/3]01 = 1/3   b) ∫231/x2dx [-1/x]23 = -1/3 +1/2 = 1/6   c) ∫12x2dx =…

Q: Which of the following represents a correct substitution used to compute: a2 da 4 sec2 (0) de a) O…

A:

Q: f sin e-cos = -1/3, what is the value of sin 2 0?

A: Since multiple questions are asked I am answering first question

Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: find coso between u and v u3(cos ,sin- 3T v=(cos ,sin 4 4 Select one: a. -.258 b. .6 C. .58 d. .8

A: We have to find the cos angle  between  the given 2 vectors.

Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: Determine the corresponding reciprocal ratio that corresponds to cos e= 0.8. 5 sec e= 4 c. sec e= a.…

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

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

A:

Q: Compute the indicated quantity using the following data. 12 sin a = 13 where = < a < T 2 cos B 3…

A:

Q: The power P in a circuit is P = Ri2, where R is the resistance and i is the current. Find dP/dt at t…

A: P=Ri2 , i=sin4πt Now substituting i=sin4πt in P=Ri2, we get P=Rsin4πt2 Now differentiating with…

Q: e cos a sin a da

A:

Q: Which expression is equivalent to cot a(sec a - 1)(sec a + 1) for all values of a for which cot…

A:

Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

Q: If cos A with A in QIV , find sec %3D a. sec | b. sec 2. с. sec A d. sec 4-5 %3D A sec e. A2 1/2 II…

A: Since you are asking multiple questions. We are answering only the first question. Given, cosA=18…

Q: Using Simpson's rule, the approximation value for the o sin(x)dæ is : Select one: a. 1.024 b. 0.425…

A:

Q: <O< 2T, sec(0)=9/4, find sin(0)=_ Suppose that places) (round to 3 decimal 2

A:

Q: Express the following function in terms of ‘Sine & Cosine’; y (t) = 4 sin 2πt + 15 cos 2πt

A: Topic- trigonometry basics

Q: 3 t coso ,3 sin 0 sing dr d0 do /2 0, 0.

A:

Q: 3. cos?wt

A:

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

A:

Q: 9. Decide whether or not the following equations are true or false: e° = cos" r + sin² r = cosh? r –…

A:

Q: The value of | Je A. -sin-¹ (ex) + C C. sin-¹ (e) + C dx 2x B.-sin-1 (e-2x) + C D. sin-¹ (e-2x) + C

A:

Q: Evaluate va 3 cos a sin x dx. + C

A: To find: The value of integral ∫cosxsin3xdx. Formula used: The trigonometric relation is…

Q: Use the linearization of f(x) = sin x about an appropriate point Xo to approximate sin 610. Note…

A:

Q: 15. f(t) = e" sin bt

A: Given function f(t) = eat sin(bt)

Q: The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is…

A: The position of an object,st=14cos4t-16sin4t on the interval 0&lt;t&lt;3

Q: The f sec$30 sin 30 d0 is {A} sec*30 + C 12 {C}-cos*30 + C {D}cos 30 + C 12 {B} sec 30 + C 18 18

A:

Q: Find fo, fe fe if fp.0,4) p cos sin 0 %3D

A:

Q: FIND SIN' A WHERE A= at b

A:

Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: f(t) = -3+4 cos(,(t – 3 ).

A:

Q: tan 20 10. lima-0 A. 0 B. 2 C. 4 D. 0 %3D sin e

A: We will answer the first question specified by you. Please resubmit the question specifying the one…

Q: Find cos(A - B). cos A = V10 and sin B = ,where 0° <A<90° and 270° <B< 360°. 10 O V10-3 30 20 O…

A: Given query is to find cos (A-B).

Q: Two identical tuning forks are struck, one a fraction of a second after the other. The sounds…

A: Given The sounds produce by tuning forks are modeled by f1t=Csinωtf2t=Csinωt+α The two sound waves…

Q: 1. Find the exact val a) sin 3π 2 b) cot (210°) c) sec (-765°)

A: topic:- trigonometry  note:- As per our guideline if more than one question posted than only first…

Q: Next Rewrite 5 sin(x) +2 cos(x) A sin(x + 4) as A = Note: o should be in the interval -T < O < T II…

A: sin(A+B) = sin(A) cos(B) + cos(A) sin(B)

Q: Coтрule the mtegral sin r dr т — 4г + 5

A: This would be solved using catchy integral theorem.

Q: /2 cos a sin(sin r) dx

A: using method of substitution

Q: y = sin x coS X 4

A: Given data:     The given equation is: .   The given expression can be written as,

Q: Using an appropriate substitution, f sinº (x)cos'(x)dx is equal to: cosl +C 11 cos 11 O Ths opton O…

A: We will find the integral by substitution as following-

Q: Find the current in the RLC-circuit when inductance is 0.1 H; resistance is 20 ohms, C = 0.0002…

A:

Q: derivation is required

A:

Q: A certain substitution gives S sin*x)cos"(x)dx = S (u²-u*)du .what is n?

A: For substitution- Balancing the above equation, we can solve it as follows-

Q: Find the GS of: (r + sin e - cos e)dr + r(sin e +cos E)dO =0 O r2+2r(sine - cos©+C=0 Or2-2r(sine -…

A:

Q: Find the equation of a sine wave in the form y = a sin(x + c) +d that is obtained by shifting the…

A: The given function is: y=sin(x)

Q: b. tan(a + B); cos(a) = 13 for a in quadrant III and sin(B) = 63 for B in quadrant IV %3D 85 65

A:

Q: (b) /(cos æ)* sin a da

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.