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Substitution Rule Applied to Indefinite Integrals01:27

Substitution Rule Applied to Indefinite Integrals

When a force is applied to a linear spring, the restoring force increases proportionally with the amount of displacement. This behavior is described by Hooke’s law, which allows the work done on the spring to be determined directly from the force–displacement relationship. In this case, the force varies in a simple and predictable manner, making the calculation relatively simple.On the other hand, a nonlinear spring does not obey Hooke’s law. Its restoring force depends on...
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Substitution Rule Applied to Definite Integrals01:24

Substitution Rule Applied to Definite Integrals

When evaluating a definite integral whose integrand matches the structure of a composite function, the substitution method provides an efficient way to simplify the calculation. This method is based on reversing the chain rule from differentiation, allowing a complicated expression to be rewritten in a simpler form. When the integrand contains an inner function and its derivative, substitution naturally reduces the complexity of the problem.The core idea of substitution for definite integrals...
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Empathy02:34

Empathy

Some researchers suggest that altruism operates on empathy. Empathy is the capacity to understand another person’s perspective, to feel what he or she feels. An empathetic person makes an emotional connection with others and feels compelled to help (Batson, 1991). Empathy can be expressed in several ways, including cognitive, affective, and motor. 
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In- and Out-Groups01:31

In- and Out-Groups

People all belong to a gender, race, age, and social economic group. These groups provide a powerful source of our identity and self-esteem (Tajfel & Turner, 1979) and serve as our in-groups. An in-group is a group that we identify with or see ourselves as belonging to.
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Vision01:24

Vision

Vision is the result of light being detected and transduced into neural signals by the retina of the eye. This information is then further analyzed and interpreted by the brain. First, light enters the front of the eye and is focused by the cornea and lens onto the retina—a thin sheet of neural tissue lining the back of the eye. Because of refraction through the convex lens of the eye, images are projected onto the retina upside-down and reversed.
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Base Excision Repair01:54

Base Excision Repair

One of the common DNA damages is the chemical alteration of single bases by alkylation, oxidation, or deamination. The altered bases cause mispairing and strand breakage during replication. This type of damage causes minimal change to the DNA double helix structure and can be repaired by the base excision repair (BER) pathways. BER corrects damaged DNA sequences by removing the damaged base and restoring the original base sequence using the complementary strand as a template.
The first step of...
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