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2. Evaluate the following indefinite integrals. (a) ? 1 / (9 + x^2)^(5/2) dx (Hint: Use an appropriate substitution first.) (b) ? tan?¹(?x) dx (Hint: Use an appropriate substitution first.) (c) ? (x² - 9x + 39) / ((2x + 1)(x² - 2x + 5)) dx 3. Find the area of the region bounded by the curve y = ?x, the line y = 2 - x and the x-axis. 4. An investment produces a continuous income stream at the rate of I(t) = 3000 - 10t dollars per year at time t. If the prevailing annual interest rate remains fixed during the next 10 years at 7% compounded continuously, what is the present value of the investment over the next 10 years? 5. Suppose a primitive economy consists of three industries: the agricultural industry, the manufacturing industry, and the fuels industry. The corresponding technology matrix is given by A = ? 0.5 0.1 0.3 ? Agricultural ? 0.3 0.6 0.1 ? Manufacturing ? 0.1 0.2 0.4 ? Fuels Using Gaussian elimination, find the gross production of each industry if a surplus of 80 units of agricultural products, 20 units of manufactured goods, and 40 units of fuels is desired.

          2. Evaluate the following indefinite integrals.
(a) ? 1 / (9 + x^2)^(5/2) dx (Hint: Use an appropriate substitution first.)
(b) ? tan?¹(?x) dx (Hint: Use an appropriate substitution first.)
(c) ? (x² - 9x + 39) / ((2x + 1)(x² - 2x + 5)) dx

3. Find the area of the region bounded by the curve y = ?x, the line y = 2 - x and the x-axis.

4. An investment produces a continuous income stream at the rate of I(t) = 3000 - 10t dollars per year at time t. If the prevailing annual interest rate remains fixed during the next 10 years at 7% compounded continuously, what is the present value of the investment over the next 10 years?

5. Suppose a primitive economy consists of three industries: the agricultural industry, the manufacturing industry, and the fuels industry. The corresponding technology matrix is given by
A = ? 0.5 0.1 0.3 ? Agricultural
    ? 0.3 0.6 0.1 ? Manufacturing
    ? 0.1 0.2 0.4 ? Fuels
Using Gaussian elimination, find the gross production of each industry if a surplus of 80 units of agricultural products, 20 units of manufactured goods, and 40 units of fuels is desired.

2. Evaluate the following indefinite integrals.
(a) ? 1 / (9 + x^2)^(5/2) dx (Hint: Use an appropriate substitution first.)
(b) ? tan?¹(?x) dx (Hint: Use an appropriate substitution first.)
(c) ? (x² - 9x + 39) / ((2x + 1)(x² - 2x + 5)) dx

3. Find the area of the region bounded by the curve y = ?x, the line y = 2 - x and the x-axis.

4. An investment produces a continuous income stream at the rate of I(t) = 3000 - 10t dollars per year at time t. If the prevailing annual interest rate remains fixed during the next 10 years at 7% compounded continuously, what is the present value of the investment over the next 10 years?

5. Suppose a primitive economy consists of three industries: the agricultural industry, the manufacturing industry, and the fuels industry. The corresponding technology matrix is given by
A = ? 0.5 0.1 0.3 ? Agricultural
? 0.3 0.6 0.1 ? Manufacturing
? 0.1 0.2 0.4 ? Fuels
Using Gaussian elimination, find the gross production of each industry if a surplus of 80 units of agricultural products, 20 units of manufactured goods, and 40 units of fuels is desired.

Added by Debra B.

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