Use the explicit formula, b Š a 4 S (3x² - 2x+5) dx -2 n Σ f(a+k¹b-a)) (b=a] n f(x) dx = limfa+k- n→∞k=1 to evaluate the definite integral.

Q: 1. In the following exercises, evaluate each definite integral using the Fundamental Theorem of…

A: The general rule of integration is  ∫xndx=xn+1n+1+C Note:  According to the guidelines of the…

Q: Solve the definite integral using usub

A: To integrate,

Q: Find the integral +1 dr = +C

A:

Q: Determine the following integrals. f(x² −5x+6)dx a. b. 4 √(²²-27) dr dt C. √√√x³ dx d. f(x^2 + 2x +…

A:

Q: (b) 12 sec² 3x 1.² 0 6 + tan 3x dx

A:

Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Evaluate the integral dx (x + 1)(x² + 1) Sz

A: The integrand can be written as:…

Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: (a) o'x dx .. -8 x (b) dx 0 4 .. ..

A:

Q: Evaluate the integral 1 - √xé √x sec 1 2 sec | √xe¯ √x ³0c ² (2e √x - 2) dx = 2 ² (2e √x - 2) dx.

A:

Q: 1. Given the function f(x)=x -8 on [0,6] a. Sketch the function. b. Use the definition of the…

A:

Q: In the following exercise, find each indefinite integral, using appropriate substitutions. dx uV4x²…

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Q: Use the substitution a 3 sin t to evaluate the integral f V9 – x² dx.

A:

Q: /1 x² dx /2 2 x2

A: I am going to calculate this integral using trigonometric substitution.

Q: -3v3 dx V9+x?

A: Evaluate the intregal

Q: Il-Find the following integrals by suitable substitutions 1 - x. (9 + x2)) 18.dx 2- 2XVX2 + 10.dx

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Q: sin 3x (x² +16)² dx

A:

Q: Evaluate the Integral dx |. 1 + 2 ax X² 2

A: Consider the integration."Note that as per the rules, we are supposed to answer the first question…