consider the function $f(x) = 5x^8 + 4x^6 - 8x^3 - 6$.
an antiderivative of $f(x)$ is $f(x) = ax^n + bx^m + cx^p + dx^q$ where
$a$ is
and $n$ is
and $b$ is
and $m$ is
and $c$ is
and $p$ is
and $d$ is
and $q$ is

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Antiderivatives", "Power Rule for Integration" ], "current_concepts": [ "Antiderivatives", "Power Rule for Integration" ] } ## Find the general antiderivative using the power rule $$ \begin{aligned} f(x) &= 5x^8 + 4x^6 - 8x^3 - 6 \ F(x) &= \int (5x^8 + 4x^6 - 8x^3 - 6) \, dx \ F(x) &= 5 \cdot \frac{x^9}{9} + 4 \cdot \frac{x^7}{7} - 8 \cdot \frac{x^4}{4} - 6x + C \ F(x) &= \frac{5}{9}x^9 + \frac{4}{7}x^7 - 2x^4 - 6x + C \end{aligned} $$ ## Match coefficients and exponents with the given form $$ \begin{aligned} F(x) &= A x^n + B x^m + C x^p + D x^q \ A &= \frac{5}{9}, \quad n = 9 \ B &= \frac{4}{7}, \quad m = 7 \ C &= -2, \quad p = 4 \ D &= -6, \quad q = 1 \end{aligned} $$ Consider the function $f(x) = 5x^8 + 4x^6 - 8x^3 - 6$. An antiderivative of $f(x)$ is $F(x) = Ax^n + Bx^m + Cx^p + Dx^q$ where $A$ is $\frac{5}{9}$ and $n$ is 9 and $B$ is $\frac{4}{7}$ and $m$ is 7 and $C$ is -2 and $p$ is 4 and $D$ is -6 and $q$ is 1 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Antiderivatives" ] }

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Find the general antiderivative using the power rule

Match coefficients and exponents with the given form

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