The Fourier integral of the function f(x) ={ x(x - 1) ,-n n) is given by f(x)~ " (A(a) cos(ax) + B(a)sin (ax)) da Then A(a) = O A. O B. 1-cos (an) πα3 OC. 1-cos (a) a3 O D. sin(na)-a? cos(na) πα3 OE. sin(a)-a? cos(a) a3

Q: Find all solutions to tan(x)=sec(x) that lie in the domain [0, 2)

A: tan(x)=sec(x) Given interval is [0, 2).

Q: Given f(x) = determine f'(x). sin x -cos x(x+1) sin r Zaciek O (2+1)-sin c sin² T x+1 sin r (x+1)²…

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Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: Evaluate (x2 + 1) cosx dx O (x2 + 1) sin x + 2x cos x – 2 sin x + C - (x2 + 1) sin x – 2x cos x + 2…

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Q: Consider the following. cos(x + y) cos(x - y) = cos(x) - sin²(y) Prove the identity. - sin(x)…

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Q: prove that f(x) = sin*x + cos*x is a periodic function with periods

A: We use the Given Equations Prove that f(x) is a periodic function with period pie/2.

Q: +20x-22y-14-0 become when referred to the rectangul axes through the point (-2, -3), the new axes…

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Q: Make the orthagonal set of functions {1, cos(x), cos(2x), ...} orthonormal on the interval [0,2pi].

A: Two distinct functions f and g are said to be orthogonal on [a,b] if <f,g>=0   , where < ,…

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: 10 a b с d f(x) =tan(2x-n) g(x) =tan(x-n) h(x)= tan x-. ²) j(x)=tan(\/2- X

A:

Q: Evaluate / 3 x sin(x)dx 03 (sin(x) – x cos(x)) + c Osin(x) – x cos(x) + c 03 x sin(x) + 3 cos(x) + c…

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Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

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Q: Let ƒ(x) = (cos( − 4x – 5)) (sin(6x − 2)). Then ƒ'(x) =

A: f(x)=(cos(-4x-5))(sin(6x-2))

Q: find Fourier coefficients

A:

Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: What is the domain of f(x)=cos-'(In(x))? Select one: O (0,1) O (0,0) O (0,e]

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: z(r) = cos'(r)/1+r* ? cos (r) ( r Vi+r (1+r² 4 tan(r) cos'(-\/i + r*{ 4 cot(r) 1+r I tan(r) (1+r²

A: The given function is zr=cos4r1+r2.

Q: Solve using an integral cos²(x) + 2cos²( cos³(x) .dx

A: Evaluation of the integral

Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)

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.