Integrals & FTC Practice
Undo the derivative: antiderivatives rebuild a function from its rate of change. The Fundamental Theorem of Calculus turns area problems into antiderivative evaluations — with net area keeping honest count below the axis.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint; a second miss earns a stronger hint; a third miss walks you through the full solution. Scores and streaks are session-only.
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
Power-rule antiderivative
Term-by-term + C, then differentiate back to check.
FTC evaluation
Antiderivative at top minus bottom.
Negative powers
Rewrite 1/xⁿ as x⁻ⁿ first.
Trig antiderivative
Work backwards from the derivative.
Exponential
∫aeᵇˣdx = (a/b)eᵇˣ + C.
Riemann sum
Left sum: Δx times left-endpoint values.
Net area
Below the axis counts negative.
3 Watch out for these
The mistakes students make most often on these problems.
Indefinite integrals name a whole family: ∫2x dx = x² + C, never just x².
The integral is net area — symmetric regions cancel. Total area is a separate computation.
∫x³dx = x⁴/4 + C. Always differentiate your answer to check.