Exercises
Assess your integral calculus proficiency with this quiz covering essential integration concepts. Solve problems involving polynomial, exponential, logarithmic, and trigonometric antiderivatives, including x², e^x, 1/x, sin(x), sec²(x), and constants. Practice evaluating definite integrals over given intervals, calculating area under a curve, and applying the Fundamental Theorem of Calculus. Ideal for students reviewing introductory calculus, preparing for an exam, or checking their understanding of core integration rules.
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The correct answer is 1/3x³ + C because the integral of x^n is x^(n+1)/(n+1) + C where C is the constant of integration.
Integrating 2x gives x² + C, then evaluate from 0 to 2: [2² - 0²] = 4.
The integral of sin(x) is -cos(x) + C because the derivative of -cos(x) is sin(x).
The antiderivative of e^x is e^x + C since the derivative of e^x is e^x.
The integral of 1/x is ln|x| + C because the derivative of ln|x| is 1/x.
The area is 9 because the integral of f(x) = 3 over [1, 4] is 3 * (4 - 1) = 9.
The integral of a constant c with respect to x is cx + C.
Integrating x³ gives (1/4)x^4, then evaluate from 0 to 1: [1/4*1^4 - 1/4*0^4] = 1/4.
The integral of sec²(x) is tan(x) + C because the derivative of tan(x) is sec²(x).
The integral of cos(x) is sin(x). Evaluate from 0 to π/2: [sin(π/2) - sin(0)] = 1.
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