 # Calculus Problems

## Question

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## Transcribed Text

Write down the definition of the first derivative, hence differentiate the following function with respect to . f(x)=xsinx (10 marks) Using the direct method of integration, determine the value of ∫_1^3 〖2x〗^2-3x+1 dx (5 marks) By use of the Left-Hand Riemann Sum approach of ∑_(i=1)^n f(x_i^*) ∆x Where〖 x〗_i^*=a+ (∆x)i and ∆x=(b-a)/n with a and b being the lower and upper limits of the integrand respectively. Given that ∑_(i=1)^n k=nk ∑_(i=1)^n i=(n(n+1))/2 ∑_(i=1)^n i^2=(n(n+1)(2n+1))/6 Deduce the value of the integrand given. (15 marks) (10 marks)

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