Let √10.5 f(x) dx = 9, (a) (b) f(x) dx = 3 3.5 3.5 S F(X /0 f(x) dx = 2, and [² (8F(x) - 4 (8f(x) − 4) dx = 21 √3.5 X 10.5 f f(x) dx = 4. Find the following.

Q: Find f(t) if L (F) equals 20 3 S-2TTS

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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: 14 6,¹ 3 Suppose f(x) dx 3 S f(x) dx = [ 14 = 15. Find

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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: If f f(x) dx = 6, f f(x) dx = 2, and f, g(x) = -5, find f₁[2f(x) — 4g(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: d°y dx6 for the following. F(x) = x’ – 8x²+2 Find -

A: y = f(x) = x7-8x2+2 We have to find the 6th derivative of y with respect to x.

Q: 1/2 S x²√1-x²dx. 0

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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: 9 If Ef fºrex 4 f(x) dx = 33 and 9 √³⁹(x) g(x) dx = 14, find *9 fºc [4f(x) + 5g(x)] dx.

A: To find out the value of the given integration.

Q: | [10f(x) – g(x)]dx if Find 5 5 f(x)dx = 7 and g(x)dx = 6. %3D | [10f(x) – g(x)]dx = i

A:

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: Given f(x) dx 8 a

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Q: Let 11 f(x) dx = 9, 10 Find "f(e) de = [ and nd S 9f(x) - 7 dx 10 [₁ f(x) dx = 7, [1² f(x) dx = 9.…

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Q: If f(t) = (1 + 0.04)t, what is f(0)?

A: note that (any number)0 =1

Q: Given √,³ 0-12 f(x)dx = 8 and g(x)dx=-4, what is -4 4 12 √,³ (g(x) − f(x)]dx?

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Q: "S If f(x) nd f(x) dx = 3.6, find [ f(x) dx = 7.1 and dx.

A: Integral

Q: (a) x® (d) 2x7 ex (b) e¹ (c) x² √√x³ (e) x+1

A:

Q: Suppose thatƒ(x) = d/dx (1 - √x) and g(x) = d/dx(x + 2). find ∫g(x) dx

A: Given: fx=ddx1-xand gx=ddxx+2 To Find: ∫gxdx Concept: Integration is an inverse process of…

Q: f(x) = Vxe-x/2 is inc decreacing

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Q: [6f(x) – g(x)]dx = i if f(x)dx 5 and g(x)dx 10

A: