Question: Evaluate the integral ∫ (sec^2(x)) dx.
Options:
tan(x) + C
sec(x) + C
sin(x) + C
cos(x) + C
Correct Answer: tan(x) + C
Solution:
The integral of sec^2(x) is tan(x) + C.
Evaluate the integral ∫ (sec^2(x)) dx.
Practice Questions
Q1
Evaluate the integral ∫ (sec^2(x)) dx.
tan(x) + C
sec(x) + C
sin(x) + C
cos(x) + C
Questions & Step-by-Step Solutions
Evaluate the integral ∫ (sec^2(x)) dx.
Step 1: Recognize that sec^2(x) is a standard integral that you can find in integral tables or calculus textbooks.
Step 2: Recall the derivative of tan(x). The derivative of tan(x) is sec^2(x).
Step 3: Since the integral of sec^2(x) gives you the function whose derivative is sec^2(x), we can conclude that the integral is tan(x).
Step 4: Don't forget to add the constant of integration, C, because we are finding an indefinite integral.
Integration of Trigonometric Functions – This concept involves finding the antiderivative of trigonometric functions, specifically recognizing that the integral of sec^2(x) is a standard result.
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