DP Mathematics HL Questionbank

• Syllabus

6.4

Sub sections and their related questions

Indefinite integration as anti-differentiation.

• 09N.1.hl.TZ0.7b: Find $\int {{{\tan }^3}x{\text{d}}x}$ .
• 13N.2.hl.TZ0.10: By using the substitution $x = 2\tan u$, show that...
• 18M.2.hl.TZ1.5a: Given that $2{x^3} - 3x + 1$ can be expressed in the...
• 18M.2.hl.TZ1.5b: Hence find $\int {\frac{{2{x^3} - 3x + 1}}{{{x^2} + 1}}} {\text{d}}x$.

Indefinite integral of ${x^n}$ , $\sin x$ , $\cos x$ and ${{\text{e}}^x}$ .

Other indefinite integrals using the results from 6.2.

• 15M.1.hl.TZ1.3a: Find $\int {(1 + {{\tan }^2}x){\text{d}}x}$.
• 15M.1.hl.TZ1.3b: Find $\int {{{\sin }^2}x{\text{d}}x}$.
• 15M.1.hl.TZ1.6c: Hence, write down $\int {\frac{{3x - 2}}{{2x - 1}}} {\text{d}}x$.

The composites of any of these with a linear function.