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To answer this question we observe that y is the product of x^2 and sin(x), so we use the product rule. Then dy/dx = 2x * sin(x) + cos(x) * x^2 The resulting equation can be tidied up by factoring out x a...

To solve this integral you should use the integration by parts formula, which is uv - integral of vu'. First let x^2 be u, therefore u'(the differential of x^2) = 2x, v' = e^x and therefore v (integral of...

1/2

This is a common question among A-Level Maths students, as integration by parts requires 2 things: 1. Something to integrate ; 2. Something to differentiate. In ln(x), we can immediately see that ln(x) is...

12th term = a + (12 - 1)*d = 2 + 11(3) = 35

Sum (9) = 9/2 [2(2) + (9 - 1)*3] = 9/2 [28] = 252/2 = 126