Question

Why do we take $\sqrt{f^2(x)} = f(x)$ when integrating by substitution?

score 200 · Answer 1 · 2022-05-13 07:41:33

200

Views

Why do we take $\sqrt{f^2(x)} = f(x)$ when integrating by substitution?

Published on 13 May 2022 - 7:41

score 164 · Answer 2 · 2022-05-22 23:21:21

164

Views

What did I do wrong in solving $\int\sec^{-1} x\,{dx}$?

Published on 22 May 2022 - 23:21

score 118 · Answer 3 · 2022-05-23 15:47:41

118

Views

How to transform triple integral $\iiint_\Omega \sqrt{1- \frac{x^2}{a^2}- \frac{y^2}{b^2} - \frac{z^2}{c^2} }\ dx dy dz$

Published on 23 May 2022 - 15:47

score 31 · Answer 4 · 2026-03-25 19:06:13

31

Views

Show that $ O((8k)!^4 \cdot\mathrm{poly}(n))=e^ { O ( \sqrt n \cdot \log n ) } $ given $ k = O( \sqrt n ) $

Published on 25 Mar 2026 - 19:06

score 122 · Answer 5 · 2022-06-02 18:59:46

122

Views

Solution to definite integration by substitution different when pulling out a constant (C4 Edexcel June 2013 Q5(b))

Published on 02 Jun 2022 - 18:59

score 82 · Answer 6 · 2022-06-03 19:32:14

82

Views

Using Integration By Parts for $\int\sec^2(x)\tan(x)\,\mathrm dx$

Published on 03 Jun 2022 - 19:32

score 102 · Answer 7 · 2022-06-05 10:39:11

102

Views

Why do you need to perform integration by substitution when integrating $\frac{1}{1+\sqrt{x}}$?

Published on 05 Jun 2022 - 10:39

score 42 · Answer 8 · 2022-06-13 08:37:23

42

Views

Simplifying equations of partial derivatives by substitution

Published on 13 Jun 2022 - 8:37

score 42 · Answer 9 · 2026-03-31 04:00:14

42

Views

Prove the logarithm property $\ln(\frac 1a) = -\ln(a)$ using its definition of fundamental theorem of calculus (FTC).

Published on 31 Mar 2026 - 4:00

score 94 · Answer 10 · 2022-06-22 23:20:55

94

Views

show integrals are equivalent

Published on 22 Jun 2022 - 23:20

score 75 · Answer 11 · 2022-06-24 12:14:31

75

Views

Simplifying atan(x)-atan(y)

Published on 24 Jun 2022 - 12:14

score 83 · Answer 12 · 2022-06-25 18:37:43

83

Views

Why group is primitive

Published on 25 Jun 2022 - 18:37

score 100 · Answer 13 · 2022-07-10 21:22:32

100

Views

Integral $\int_0^\infty x^ne^{-x} dx$

Published on 10 Jul 2022 - 21:22

score 93 · Answer 14 · 2022-07-16 14:13:20

93

Views

Calculate an indefinite integral

Published on 16 Jul 2022 - 14:13

score 197 · Answer 15 · 2022-07-16 14:51:06

197

Views

Cauchy formula for repeated integrations

Published on 16 Jul 2022 - 14:51

List Question

Why do we take $\sqrt{f^2(x)} = f(x)$ when integrating by substitution?

What did I do wrong in solving $\int\sec^{-1} x\,{dx}$?

How to transform triple integral $\iiint_\Omega \sqrt{1- \frac{x^2}{a^2}- \frac{y^2}{b^2} - \frac{z^2}{c^2} }\ dx dy dz$

Show that $ O((8k)!^4 \cdot\mathrm{poly}(n))=e^ { O ( \sqrt n \cdot \log n ) } $ given $ k = O( \sqrt n ) $

Solution to definite integration by substitution different when pulling out a constant (C4 Edexcel June 2013 Q5(b))

Using Integration By Parts for $\int\sec^2(x)\tan(x)\,\mathrm dx$

Why do you need to perform integration by substitution when integrating $\frac{1}{1+\sqrt{x}}$?

Simplifying equations of partial derivatives by substitution

Prove the logarithm property $\ln(\frac 1a) = -\ln(a)$ using its definition of fundamental theorem of calculus (FTC).

show integrals are equivalent

Simplifying atan(x)-atan(y)

Why group is primitive

Integral $\int_0^\infty x^ne^{-x} dx$

Calculate an indefinite integral

Cauchy formula for repeated integrations

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