1. Which of the following is incorrect? a. b. [(f(x) · g(x)) dx = [ f(x) dx . [ g(x) dx [(f(x) + g(x)) dx = [ f(x) dx + [g(x) dx C. c. / x² dx = 1₁x²+¹+c [d(F(x)) = F(x) + C d. C

Q: Given that (a) (b) Prx [ FLX f(x) dx = 3 and f(x) dx 2 [²(x [²Px) dx - [Px) dx f(x) f(x) f(x) dx =…

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Q: f(x) dx = -4, f(x) dx = 6, g(x) dx = 8 - If g(x) dx b. c. 3f(x) dx d. dx x) - g(x)] dx g(x)] dx e.…

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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: (a) Show that Ye(x) = Ce¯[ P(x)dx

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Q: 12 If [" f(x) dx = 19 and ' [₁ f(x) dx [R²F(x) f(x) dx = 4, find the following.

A: We can answer the question as below using the properties of definite integral.

Q: What is the value of f(x)dx; if ca+1 2 S* f(x)dx = ?

A: Integration

Q: Use the Fundamental Theorem to show that the following are true.

A: Recall the Fundamental theorem of calculus that ∫abfxdx=Fb-Fa.

Q: If f(x) = g(x) J. (Ax) + g(x)]dx= + 7 for 3<xs 5, then

A: givenf(x)=g(x)+7thenI=∫35[f(x)+g(x)]dxsubstitute value of f(x)I=∫35[g(x)+7+g(x)]dxI=∫35[2g(x)+7]dx

Q: Given that 2 < f(x) <4 for 1 <x< 2, estimate the value of | f(x)dx f(x)dx <

A: Since we have 2≤f(x)≤4 for 1≤x≤2, we have to estimate the value of ∫12f(x)dx.

Q: Is the attached question true or false? Please explain.

A: To show the below property is true or false:

Q: If a function h satisfies h(-x) = h(x) for every number x in its domain, then h is called an even…

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Q: (c) [ √4x² X -dx

A: The given integration is

Q: If f(x) is an even function, and if f³ 6f(x) dx = 15, find ſ³₂ f(x) dx. -3

A: Here we have to find the integral.

Q: Evaluate. 3 Lox f(x) dx, f(x) = (−x + 1, x≤2 1-x² + 6x-9, x>2

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Q: Find the value of +5 f(x) is odd, and ₂ f(x) dx = 5 -5 √₂ f(x) dx = f(x) dx, given than

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Q: Given the following function: f(x) = 2x For g(x) f(x) dx, determine g(x).

A: Given,       fx=2x       gx=∫fxdx

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: If f is an odd function, why is S, f(x) dx = 0?

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Q: -2x let f (x) = 3x · e¯¯

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Q: 49 |'xf(x?) dx. If f is continuous and f(x) dx = 16, find

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Q: 1. Let G(x) = | V³ +1dt. (a) Is the FTC II needed to calculate G(4)? (b) Is the FTC II needed to…

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Q: E(1|X-x)=? (ocx

A: marginal of xf(x)=∫f(y)dymarginal of yf(y)=∫f(x)dxf(y/x)=f(x,y)f(x)and E(y/x)=∫yf(y/x)dy