Questions
MCD2130 - T2 - 2025 MCD2130 Sample Test 3
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Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(15x2+2)5x3+2x+7]\displaystyle\int{\left(15\,x^2+2\right)\,\sqrt{5\,x^3+2\,x+7}} [math: dx] . [math: u=] [input] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(15x2+2)5x3+2x+7]\displaystyle\int{\left(15\,x^2+2\right)\,\sqrt{5\,x^3+2\,x+7}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 2
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Step-by-Step Analysis
To tackle this integral, we need to identify a substitution that simplifies the square root part and then relate the differential consistently.
Option set for part a): The inner expression under the square root is 5x^3 + 2x + 7, so a natural substitution is u = 5x^3 + 2x + 7. This choice aligns the derivative du/dx with the remaining polynomial factors in the integrand, setting up a clean substitution.
Option set for part b): If u = 5x^3 + 2x + 7, then differen......Login to view full explanationLog in for full answers
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Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(10x+2)5x2+2x+7]\displaystyle\int{\left(10\,x+2\right)\,\sqrt{5\,x^2+2\,x+7}} [math: dx] . [math: u=] [input] Your last answer was interpreted as follows: [math: 5x2+2x+7] 5\,x^2+2\,x+7 The variables found in your answer were: [math: [x]] \left[ x \right] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(10x+2)5x2+2x+7]\displaystyle\int{\left(10\,x+2\right)\,\sqrt{5\,x^2+2\,x+7}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 19
Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(15x2+5)5x3+5x+5]\displaystyle\int{\left(15\,x^2+5\right)\,\sqrt{5\,x^3+5\,x+5}} [math: dx] . [math: u=] [input] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(15x2+5)5x3+5x+5]\displaystyle\int{\left(15\,x^2+5\right)\,\sqrt{5\,x^3+5\,x+5}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 2
Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(10x+5)5x2+5x+5]\displaystyle\int{\left(10\,x+5\right)\,\sqrt{5\,x^2+5\,x+5}} [math: dx] . [math: u=] [input] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(10x+5)5x2+5x+5]\displaystyle\int{\left(10\,x+5\right)\,\sqrt{5\,x^2+5\,x+5}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 19
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