Chapter 6 Homework

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Chapter 6 Homework

1. Find the indefinite integral

$\int \sqrt{2 x + 1} d x$

2. Evaluate the Definite Integral

$\int_{0}^{1} 20 x {(2 x + 1)}^{4} d x$

3. Evaluate the definite integral

$\int_{0}^{2} \frac{x}{x^{2} + 1} d x$

4. Find the function f given that the slope of the tangent line to the graph at the point (1, 1) is

f ‘ (x) = 3 x^{2} - 4 x + 1

5. Find the function f given the slope of the tangent line to the graph at the point (1, -2) is

f ‘ (x) = \frac{\ln x}{x}

6. Let

f (x) = - 2 x^{2} + 1

and compute the Riemann sum of f over the interval [1, 2] by partitioning the interval into five subintervals of the same length ( n = 5 ) , where the points

p i (1 \leq i \leq 5)

are taken to be the right endpoints of the respective subintervals.

7. Find the area of the region under the curve

y = e^{2 x} f r o m x = 0 t o x = 2

8. Find the area of the region bounded by the curve

y = - x^{2} - x + 2

and the x – axis.

9. Find the area of the region bounded by the graphs of the function

f (x) = e^{x} a n d g (x) = x a n d t h e v e r t i c a l l i n e s x = 0 a n d x = 2

10 Chi-Tai plans to deposit $4,000 / year in his defined benefit retirement account. If interest is compounded continuously at the rate of 8% / year, how much will he have in his retirement account after 20 years.

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This question is taken from Math 238 – Calculus for Business and Social Sciences » Spring 2022 » Homeworks

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