Question 1
Evaluate $\int_{0}^{\pi/2} 3\cos(x) \, dx$.
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Mathematical Methods Β· Unit 3 Β· Introduction to integration Β· Anti-differentiation
Use the formulas β« sin (π₯) ππ₯ = β cos(π₯) + π and β« cos(π₯) ππ₯ = sin (π₯) + π.
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Question 2
F(x) = β«(5sin(x) + 3cos(x)) dx. Use integration to determine F(x), if F(0) = 2.
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Question 3
A particle moves along a straight line with velocity v(t) = 3sin(t) + 2cos(t) metres per second, where t is the time in seconds since t = 0. Determine the displacement of the particle from t = 0 to t = Ο, given that the particle is at the origin when t = 0.
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