consider the function $f(x) = 2x^{10} + 6x^5 - 4x^4 - 1$.

enter an antiderivative of $f(x)$. do not enter $+c$ as part of your answer.

Question

consider the function $f(x) = 2x^{10} + 6x^5 - 4x^4 - 1$.

enter an antiderivative of $f(x)$. do not enter $+c$ as part of your answer.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Antiderivatives", "Power Rule for Integration" ], "new_concepts": [], "current_concepts": [ "Antiderivatives", "Power Rule for Integration" ] } ## Set up the antiderivative integral $$ F(x) = \int (2x^{10} + 6x^5 - 4x^4 - 1) \, dx $$ ## Apply the power rule term by term $$ \begin{aligned} F(x) &= 2 \cdot \frac{x^{11}}{11} + 6 \cdot \frac{x^6}{6} - 4 \cdot \frac{x^5}{5} - x \ &= \frac{2}{11}x^{11} + x^6 - \frac{4}{5}x^5 - x \end{aligned} $$ Consider the function $f(x) = 2x^{10} + 6x^5 - 4x^4 - 1$. Enter an antiderivative of $f(x)$. Do not enter +c as part of your answer. Answer: $\frac{2}{11}x^{11} + x^6 - \frac{4}{5}x^5 - x$ +c { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Antiderivatives" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the antiderivative integral

Apply the power rule term by term

Answer: