Integral as an anti-derivative; fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions; integration by substitution, by parts and by partial fractions; integration using trigonometric identities; evaluation of simple integrals; fundamental theorem of calculus; properties of definite integrals; evaluation of definite integrals; determining areas of regions bounded by simple curves.
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Q1 · Integral Calculus · EASY
Evaluate the integral ∫(3x² + 4x - 5)dx.
Q2 · Integral Calculus · MEDIUM
If ∫₀^(π/2) sin²x dx = k, then the value of k is:
Q3 · Integral Calculus · MEDIUM
Using integration by parts, evaluate ∫x·e^x dx.
Q4 · Integral Calculus · EASY
The area bounded by the curve y = x², the x-axis, and the lines x = 1 and x = 3 is:
Q5 · Integral Calculus · HARD
Evaluate ∫(2x + 3)/((x + 1)(x + 2)) dx using partial fractions.