Integration tips and tricks - Math 1A, section 103
1. Find 0∫1x dx.
2. What is -3∫3√(9 - x2) dx?
3. Sometimes it helps to simplify an expression before you integrate it. Use this principal to evaluate
1∫5(x2 + 5x + 6/x2 + 3x)dx.
4. Look for familiar derivatives in other integral problems:
(a) 1∫2 2/x dx
(b) 1∫2 (3/1+x2) dx
(c) 1∫2cos(sin(x)) · cos(x) dx
5. Let's see if you can do this one without any tips. Evaluate
0∫π/3(sin(θ) + sin(θ) tan(θ)/sec2(θ)) dθ.
6. Rejoice in your newfound power of prophecy! Suppose you throw a ball upward in the air from a starting height of 2 meters and a starting velocity of 3 meters per second. Given that the Earth's gravity causes the ball to have a constant acceleration of -9.8m/s2, how long will it take for the ball to reach the ground?