Multiple Choice
Find by evaluating the following indefinite integral.
7. Antiderivatives & Indefinite Integrals
Indefinite Integrals
Struggling with Calculus?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Find by evaluating the following indefinite integral.
A
B
C
D
Verified step by step guidance1
Identify the integral to be evaluated: \( \int x^8 \, dx \). This is an indefinite integral, meaning we are looking for a function whose derivative is \( x^8 \).
Recall the power rule for integration, which states that \( \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \), where \( C \) is the constant of integration.
Apply the power rule to the integral \( \int x^8 \, dx \). Here, \( n = 8 \), so we increase the exponent by 1 to get \( x^{8+1} = x^9 \).
Divide by the new exponent to complete the integration: \( \frac{x^9}{9} \).
Don't forget to add the constant of integration \( C \) to the result, giving the final expression for \( h(x) \) as \( h(x) = \frac{x^9}{9} + C \).
5:04mWatch next
Master Introduction to Indefinite Integrals with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Indefinite Integrals practice set
Problem sets built by lead tutorsExpert video explanations