Mock Board Exam: Integral Calculus (Philippines Criteria)
INSTRUCTIONS:
1. Answer all questions.
2. Show complete solutions where applicable.
3. Write your final answers clearly.
4. Calculators allowed unless specified otherwise.
1. Evaluate the integral: int (3x^2 - 2x + 1) dx
2. Find the area under the curve y = x^3 from x = 0 to x = 2.
3. Determine the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 0, x
= 0 to x = 1 about the x-axis.
4. Solve the differential equation: dy/dx = x * y with initial condition y(0) = 1.
5. Evaluate the definite integral: int from 1 to 4 of (1/x) dx.
6. Use integration by parts to evaluate int x * e^x dx.
7. Evaluate the improper integral: int from 1 to infinity of 1/x^2 dx.
8. Find the arc length of the curve y = sqrt(x) from x = 0 to x = 4.
9. Solve int sin^3(x) dx.
10. A tank has the shape of an inverted cone with height 4 m and radius 2 m. Find the work required
to pump water to the top if the tank is full. (Assume rho = 1000 kg/m^3 and g = 9.8 m/s^2)
INSTRUCTIONS:
1. Answer all questions.
2. Show complete solutions where applicable.
3. Write your final answers clearly.
4. Calculators allowed unless specified otherwise.
1. Evaluate the integral: int (3x^2 - 2x + 1) dx
2. Find the area under the curve y = x^3 from x = 0 to x = 2.
3. Determine the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 0, x
= 0 to x = 1 about the x-axis.
4. Solve the differential equation: dy/dx = x * y with initial condition y(0) = 1.
5. Evaluate the definite integral: int from 1 to 4 of (1/x) dx.
6. Use integration by parts to evaluate int x * e^x dx.
7. Evaluate the improper integral: int from 1 to infinity of 1/x^2 dx.
8. Find the arc length of the curve y = sqrt(x) from x = 0 to x = 4.
9. Solve int sin^3(x) dx.
10. A tank has the shape of an inverted cone with height 4 m and radius 2 m. Find the work required
to pump water to the top if the tank is full. (Assume rho = 1000 kg/m^3 and g = 9.8 m/s^2)
