What is the antiderivative of sin²(x)?
Answer: The antiderivative of sin²(x) can be expressed as (x/2) – (1/4)sin(2x) + C, where C is the constant of integration.
Exploring Antiderivatives
Antiderivatives, or indefinite integrals, represent the reverse process of differentiation in calculus. The antiderivative of sin²(x) is found using trigonometric identities and integration techniques. It’s a crucial concept in calculus, providing a way to calculate areas, volumes, and solve physics problems involving motion. Understanding antiderivatives is fundamental for students and professionals in fields such as engineering, physics, and mathematics.
FAQ on Exploring Antiderivatives
What is the antiderivative of cos(x)?
The antiderivative of cos(x) is sin(x) + C.
What is the antiderivative of x²?
The antiderivative of x² is (1/3)x³ + C.
What is the antiderivative of e^x?
The antiderivative of e^x is e^x + C.
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