Answer the following with complete justification:

PHYSICS · Multi-part · ISC · Physics · Current Electricity · Ohm's law, V-I graphs and ohmic/non-ohmic conductors

Problem

Answer the following with complete justification: (i) Evaluate ∫6x2tan⁡(x3)sec⁡2(x3) dx.\displaystyle \int 6x^{2}\tan\bigl(x^{3}\bigr)\sec^{2}\bigl(x^{3}\bigr)\,dx. (ii) Hence, find ∫016x2tan⁡(x3)sec⁡2(x3) dx.\displaystyle \int_{0}^{1} 6x^{2}\tan\bigl(x^{3}\bigr)\sec^{2}\bigl(x^{3}\bigr)\,dx.

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