If cos? 0 – 3 cos 0 + 2 = sin² 0 and 0 an acute angle, then the value of (4 cot 0 + 2 csc 0) is V3 8. 3 (3 4 4 Option 1 Option 2 2V3 4V3 Option 3 O Option 4

Q: If F(x) is an antiderivative of x2 +x', then what is the value of F(1) - F(-1)? A) -1 B) -2 D) 3

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Q: 10* -dx may be written as Aln secB*+ tanB*| +C. where A, B, and C are constants not equal to zero. E...

A: ∫10xcos 10xdx Substitute 10x=u⇒10xln 10 dx=du⇒10xdx=1ln 10du =∫1ln 10ducos u=1ln 10∫sec u du=1ln 10l...

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Q: dx - = In[F(x)]+C•What is f(/3) For if C = 0? (x+x³) (x Tan-!x+ 1)

A: A detailed solution is given below

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Q: Use the Trapezoidal Rule to approximate the area under the curve f(x) = 4x2 – x on the interval [2, ...

A: The given function is; f(x)=4x2-x.

Q: Question 3 The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies ...

A: ∫-b-a1+xfxxdx = ∫-b-a1xdx +  ∫-b-afxdx = lnx]-b-a + ∫-b-afxdx Given ∫fxdx = Fx and Fx is odd functio...

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Q: b. d xP +C. What is the value of the sum a The general antiderivative of (3x2-4) 2x2 can be written ...

A: ∫(3x2-4)2x2dx=∫(9x6-24x4+16x2)dx                             =97x7-245x5+163x3+c

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Q: cos2x- sin2x cos2x dx =-F(x)+C: What is F(x)? For cosx-sinx 1 A (sinx- cosx -3 sinx + -cosx+ cosx+ -...

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Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

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Q: cos2x – sin2x cos2x dr%3D 3 For -dx =-F(x) + C- What is F(x)? cosx – sinx (sinx – cosx) 2 2 sinx +-c...

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Q: 10* dx may be written as Aln secB+ tanB*+ C. where A, B, and C are constants cos10 not equal to zero...

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Q: If F (x) is an antiderivative of x-2+x-1, then what is the value of F(1) – F (– 1)? 3 -1 -2

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Q: 8969 2. find 121 detA)? OY

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Q: 6. . Suppose that Y,,Y,..Y, form a random sample from a distribution for which the p.d.f. is as foll...

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Q: The general antiderivative of (3x2-4)2x2 can be written as What is the value of the sum of a+b+d+m +...

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Q: 1 If- csc 0 – 1 + csc 0 + 1 1 = 2 sec 0, and 0 and acute angle, then the value of (cot 0 + cos 0) is...

A: topic - trigonometric identities

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: 18. Which of the following integrals is equal to the integral s(3x-5) dr? 3ו7. A. 2 |dz 3 В. -2 f(2)...

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Q: What is the integrable form of sin-cos- sin0 do?

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Q: dx = In[F(x)]+C.What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1)

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Q: dx For (x+x³) (xtan-1(1) +1) =n(F(x))+C. What is F (/3) if C=0? A

A: Integrate the function to find F(x).

Q: 2 Find the area of the region bounded by the curve y2 =4x and the lines x = 1 and x = 4. A. 24 squar...

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Q: 1. List the first five terms of the sequence (-1)"-1n An n! + 3 n > 1.

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Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4.

A: The given curve is y2=4x and lines x=2 and x=4. From the given information,