Given f²³ F(x (a) [ 1(x) dx. f(x) dx = 16 and (b) [ f(x) f(x) dx. 5 (c) [³1x) dx. f(x) 5 (d) [²² X 2f(x) dx. [₁ f(x) dx = 9, evaluate

Q: (12) Find the Value of b such that: [3x² dx = 27 (A) 6 (C) 9 (B) 3 (D) none of these 4

A: Step 1:To find the value of b such that ∫0b​3x2dx=27, we need to solve the definite integral: Step…

Q: If f(x) is even and 5 [₁(f(x) - f(x) 8) dx = 8, find -5 5 [²³F(x) f(x) dx.

A: ∫-55fx-8dx=8 ∫-55fxdx-∫-558dx=8 ∫-55fxdx-8∫-55dx=8 As, ∫dx=x ∫-55fxdx-85--5=8 ∫-55fxdx-8×10=8…

Q: (e + x + 2)dx 3.

A: The sum rule for integration states that ∫fx+gxdx=∫fxdx+∫gxdx. The integration formula for…

Q: Given f(x) dx = 6 and g(x) dx = -4, evaluate the following. %3D (a) [f(x) + g(x)] dx (b) [g(x) –…

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Q: (x² for x < 2 Evaluate: g(x)dx where g(x) =16 – x for x 2 2

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Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

A:

Q: I. | f(x) dx = 14 and Jo f(x) dx = 6, evaluate J5 Given (a) /R f(x) dx. Jo (b) f(x) dx. /5 (c) f(x)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: x +1 dx | (25 – 12) 3 2

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Q: a) Find fxVx + 2 dx b) Find fevx dx c) Find x3 In x dx

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Q: (c) [ √4x² X -dx

A: The given integration is

Q: Use the values 3 1³ F(x 16 90 f(x) dx = 6 and g(x) dx = 2 to evaluate the definite integral.

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Q: ,2 So|x² - 1 dx

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Q: 1/2 S x²√1-x²dx. 0

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Q: (3 − |x|)dr is equal to L (3 (a) f( (3 - x) dx (b) [(3+z)dz (c) [²₁ (3 - x) dx + [² (3 + x) dx (d)…

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Q: need

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Q: Find | [3f(x) – g(x)]dx : i if 6 f(x)dx 2 and g(x)dx = 30 %3D %3D

A: Given: I=∫163fx-gxdx And ∫16fxdx=2 ; ∫16gxdx=30 We know that; the sum rule: ∫fx±gxdx=∫fxdxdx±∫gxdx…

Q: Given that (a) (b) [{f(x) dx = 7 and ['f(x) [₁Fx f(x) dx [²F(x) dx - [₁1x) f(x) dx f(x) dx = 9,…

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Q: ·S In (x) vxln(x)-x X dx

A: We know that integration power rule is - Integration of xn is xn+1/n+1 + C . Here C is integration…

Q: A) a B) b ²¹dx = √( + g(x)) dx, then A + √² g(x) dx is equal to x³+x A. -1 B. −1+In(5/2) C. 1 D. -1…

A: Given; ∫x2-1x3+xdx=∫Ax+gxdx   As we know that; ∫1ax+bdx=1alnax+b+C

Q: 1ƒ(x) == F(x), dx F(x), which of the following is equal to F(Arcsecx)? dx 1 (+) O F(x) = + f(x)…

A: If fx=ddxFx, then to determine the expression which is equal to ddxFArcsec x.

Q: X x²-x+ 20 3 X để nghi + 5x dx

A:

Q: Find (x + 2)(x-7)dx (x + 2)(x − 7)dx= + C

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Q: √₁² x (1 – x²) dx

A: Topic = Integration

Q: Find f(x) such that • ff(x) dx = 1/√ √ x² + 4 + C

A: