1.
Separation of Variables: The goal is to isolate y and t on separate sides of the equation. To do this, you're essentially integrating with respect to t on both sides. The left side has dy/dt and dt, so you can think of it as integrating dy with respect to y, and the right side is integrating dt with respect to t.
2.
Integrating with Respect to t: The integral of dy/dt with respect to t is simply y because the derivative of y with respect to t is dy/dt. So, ∫1/g(y)(dy/dt)becomes ∫1/g(y)dy. This step involves a change of variables from t to y, and the dt terms effectively cancel out.
3.
Integrating the Right Side: Similarly, integrating h(t) with respect to t on the right side just yields ∫h(t)dt.
1.
Separation of Variables: The goal is to isolate y and t on separate sides of the equation. To do this, you're essentially integrating with respect to t on both sides. The left side has dy/dt and dt, so you can think of it as integrating dy with respect to y, and the right side is integrating dt with respect to t.
2.
Integrating with Respect to t: The integral of dy/dt with respect to t is simply y because the derivative of y with respect to t is dy/dt. So, ∫1/g(y)(dy/dt)becomes ∫1/g(y)dy. This step involves a change of variables from t to y, and the dt terms effectively cancel out.
3.
Integrating the Right Side: Similarly, integrating h(t) with respect to t on the right side just yields ∫h(t)dt.
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Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
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Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong71