Difference between revisions of "Science:Math Exam Resources/Courses/MATH105/April 2017/Question 01 (g)/Solution 1"

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Note that the derivative of <math> e^{x^4+1} =4x^3 e^{x^4+1}. </math>
 
Note that the derivative of <math> e^{x^4+1} =4x^3 e^{x^4+1}. </math>
Thus <math>\int_{-2}^{1} x^3 e^{x^4+1}dx = \int_{-2}^{1} de^{x^4+1}= \frac{1}{4} [ e^{x^4+1} ]_{-2}^{1}=</math> <math>\color{blue}\frac{1}{4}(e^2-e^{17}). </math>
+
Thus <math>\int_{-2}^{1} x^3 e^{x^4+1}dx = \frac{1}{4} \int_{-2}^{1} de^{x^4+1}= \frac{1}{4} [ e^{x^4+1} ]_{-2}^{1}=</math> <math>\color{blue}\frac{1}{4}(e^2-e^{17}). </math>

Latest revision as of 22:16, 8 March 2018

Note that the derivative of Thus