Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) x3 dx, x = 3 tan(0) 3(2 + 0)(}) - 9( ? +1) Sketch and label the associated right triangle. 3 x² – 9 V9- x? Vx² +9 x + 9 3 3. 3.

Q: Use the Fundamental Theorem of Calculus to evaluate each of the following integrals. 3 (a)…

A: Evaluate the given integrals

Q: Evaluate the integral. √x (x². - 49)³/2 dx

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Q: sec? x etanx dx 8. V1 + etanx

A: Let us assume:u=1+etanxdu=0+etanx·d(tanx)du=sec2x·etanxdx

Q: Evaluate the definite integral. (4y° - 3) dy 8. 2. 1 - (4y° - 3) dy = (Simplify your 8. 9. 2. -1

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Q: Evaluate the definite integrals using (a) integration, (b) trapezoidal rule, (c) the mid-ordinate…

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Q: Find y in terms of x. dy =x+ 5, curve passes through (0, 14) Select one: O A.y =x+ 5x +14 B.y = x +…

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Q: Evaluate sin (3x) dx using integration by parts / Tabular Method.

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Q: Calculate the definite integral of:

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Q: Evaluate the definite integral. 6. e2x dx e2x + 3

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Q: Concept Check 3 Evaluate the following integrals and simplify your answers. 1.5(4cscxcotx+2 sec²x)dx…

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Q: sin x-1 x+cos x -dx

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Q: sinx 6. S dx cos² x

A: Integration

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.