Integration techniques, definite integrals, areas and basic differential equations.
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Q1 · Integral Calculus and Differential Equations · EASY
Evaluate the definite integral: ∫₀¹ (3x² + 2x) dx
Q2 · Integral Calculus and Differential Equations · EASY
Find ∫ (1/x) dx, where x > 0.
Q3 · Integral Calculus and Differential Equations · MEDIUM
The area bounded by the curve y = x², the x-axis, and the lines x = 0 and x = 2 is:
Q4 · Integral Calculus and Differential Equations · MEDIUM
Solve the differential equation dy/dx = 2x, given that y = 3 when x = 1.
Q5 · Integral Calculus and Differential Equations · HARD
Evaluate ∫ sin(2x) cos(2x) dx using substitution.